Research ArticleThe Integrated Fuzzy AHP and Goal Programing ModelBased on LCA Results for Industrial Waste Management byUsing the Nearest Weighted Approximation of FNAluminum Industry in Arak Iran

Ramin Zare1 Jafar Nouri1 Mohammad Ali Abdoli2 Farideh Atabi3 and Majid Alavi4

1Department of Environmental Management Graduate School of Environment and Energy Islamic Azad UniversityScience and Research Branch Tehran 1477893855 Iran2Faculty of Environment University of Tehran PO Box 14155-6135 Tehran 3836119131 Iran3Department of Environmental Engineering Graduate School of Environment and Energy Islamic Azad UniversityScience and Research Branch Tehran 1477893855 Iran4Department of Mathematics Islamic Azad University Arak Branch Arak Iran

Correspondence should be addressed to Jafar Nouri nourijafargmailcom

Received 16 July 2015 Accepted 16 November 2015

Academic Editor Steve Bull

Copyright copy 2016 Ramin Zare et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The worldwide recycled aluminum generation is increasing quickly thanks to the environmental considerations and continuousgrowing of use demands Aluminum dross recycling as the secondary aluminum process has been always considered as aproblematic issue in theworldThe aimof this work is to propose amethodical and easy procedure for the proposed system selectionas the MCDM problem Here an evaluation method integrated FAHP is presented to evaluate aluminum waste managementsystemsTherefore we driveweights of each pair comparisonmatrix by the use of the goal programming (GP)modelThe functionalunit includes aluminum dross and aluminum scrap which is defined as 1000 kilograms The model is confirmed in the caseof aluminum waste management in Arak For the proposed integrated fuzzy AHP model five alternatives are investigated Theresults showed that according to the selected attributes the best waste management alternative is the one involving the primaryaluminum ingot 995 including 200 kg and the secondary aluminum 98 (scrap) including 800 kg and beneficiation activitiesare implemented duplicate aluminum dross is recycled in the plant and finally it is landfilled

1 Introduction

Nowadays aluminum is used in industry transportation andconstruction and packaging industries more increasingly Inaluminum industries the secondary aluminum productiongrows rapidly due to the issues pertaining to the environmen-tal considerations and the rise in the consumption demandsIt is estimated that the production of this material will reach260 times 107 t in 2015 [1] In the following FAHP methodologyhas been considered to evaluate the environmental econom-ical and social impacts of the aluminumwaste To amelioratethe MCDM procedure and facilitate aluminum waste systemchoice process the present researchwill use a fuzzy integratedapproach to represent decision-makersrsquo judgments which is

utilized to evaluate the weight of criteria and alternativesThen literature the results of questionnaires overviews andthe results of the primary life cycle assessment are evaluatedby experts by the use of fuzzy linguistic terms

This approach allowed us to numerically display vague-ness and to reflect the decision-makersrsquo perception of thedecision-making process as well

This research is comprised of the following sectionsIn Section 2 we give some related literature concerning

the proposed problem a once-over In Section 3 asmethodol-ogy we review some basic concepts and finally the proposedalgorithm is explained In Section 4 a case study related tothe aluminum waste is presented The study ends with adiscussion and conclusion

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 1359691 13 pageshttpdxdoiorg10115520161359691

2 Advances in Materials Science and Engineering

2 Literature Review

Total primary aluminum consumption in the world was of502Mt in 2013 [2] The manufacture of aluminum fromalumina demands much more energy than other metals andleads to major quantities of greenhouse gas pollutants [3]Aluminum production is responsible for 11 of the annualgreenhouse gas emissions [4] It is about 75 of all thealuminum production as secondary aluminum (aluminumscrap and dross) since 1880s which is still in generative useThe findings of these studies indicated that the emissions andenergy consumption of aluminumwere decreased in the pro-duction of secondary aluminum compared to the productionof primary aluminum [5] Authors represented that the alu-minum waste recycling is economically and environmentallyfriendly [6] Opportunities for recovery and recycle of metalsfrom wastes are high Recovery of secondary resources suchas Al Fe Cu and Zn from these wastes is gaining increasinginterest [7 8] Also by recycling secondary aluminumresources are saved the need for landfill area could have beendecreased and the public opinion would be satisfied A lotof dross is produced as a waste product during remeltingor refining aluminum [9] Although aluminum dross is awaste of current resources in case of being landfilled withoutsuitable treatment it will lead to the secondary contaminantswhich would affect air water and soil [1] Aluminum wastesmainly are disposed of in landfill sites which may resultin leaking of toxic metal ions into the ground water Alsowhen aluminum waste comes in contact with water it emitspoisonous gases as NH

3 CH4 PH3 H2 and H

2S [10 11]

The environmental effects of aluminum scrap from recycledaluminum should beminimizedThat iswhy in this study theeffects and impacts of aluminum waste management systemsare evaluated In addition aluminumdross recycling has beenalways considered as a problematic issue The fuzzy set ideawas used by [12] to manage uncertainty in the inventorydata Seppala modified and compared the fuzzy approachpresented in [13] to the ldquotraditionalrdquo valuation method ofLCA [14] Since Van Laarhoven Pedrycz and Buckley [1516] offered their initial study in FAHP numerous workshave applied FAHP in disparate environment problems [17ndash20] Also some studies applied FAHP method concerningLCA thinking For example this methodology was appliedby Zheng et al in the building sector [21] and by Chanand Lin to evaluate green product design [19 22] Complexdecision-making situations are relevant to the aluminumwaste management system which needs the realization ofdifferent sections of the industry and community Howeverlittle attention has been given to the environmental aspectsof the processing output of aluminum dross and aluminumscrap as aluminum waste in MCDMmethodologies

3 Methodology

The aim of this work is to offer a methodical and straight-forward and simple to use method for the aluminum wastemanagement system selection problem MCDM methodswere considered for this aim including fuzzy logic fuzzycomparison matrix NWIA the GP method and the fuzzyAHP

cba0

1

Figure 1 Typical triangular fuzzy number

31 Fuzzy Numbers (FN) FN are one path to explain theambiguity and be missing accuracy of data [23] A fuzzynumber is a fuzzy set 119860 119877 rarr 119868 = [0 1]119877 that satisfiedthe following

(1) ldquo119860rdquo is continuous

(2) 119860(119909) = 0 outside some interval [119886 119888]

(3) There are real numbers 119886 119887 and 119888 so that 119886 le 119887 le 119888

And

(a) 119860(119909) = 1 119909 = 119887(b) 119860(119909) is decreasing on [119887 119888](c) 119860(119909) is increasing on 119886 le 119909 le 119887

The set of all such fuzzy numbers is represented by 119865(R)Fuzzy numberwith linear sides and themembership functionhaving the following form (see Figure 1)

119860 (119883) =

119909 minus 119886

119887 minus 119886

119886 le 119909 le 119887

119888 minus 119909

119888 minus 119887

119887 le 119909 le 119888

0 otherwise

(1)

is called triangular fuzzy number and is denoted by =

(119886 119887 119888)

32 Fuzzy Pair Comparison Matrix Consider the expert thatprepares fuzzy opinion in place of exact opinion It presumestrade to be with comparison matrix with triangular FN beingthe components of the matrix We suppose a matrix whosecomponents are FN as

= (

(119886119871

11 119886119872

11 119886119880

11) sdot sdot sdot (119886

119871

1119899 119886119872

1119899 119886119880

1119899)

d

(119886119871

1198991 119886119872

1198991 119886119880

119899119899) sdot sdot sdot (119886

119871

119899119899 119886119872

119899119899 119886119880

119899119899)

) (2)

Advances in Materials Science and Engineering 3

where = (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) is a triangular FN see [24] It is

supposed that is reciprocal if the following term is satisfied[25]

119894119895= (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) forall119894 119895 = 1 119899

implies that 119894119895= (

1

1205721198801015840

119894119895

1

1205721198721015840

119894119895

1

1205721198711015840

119894119895

)

forall119894 119895 = 1 119899

(3)

33 The Nearest Weighted Interval Approximations (NWIAs)In this section we review an interval processor of FNwhich is denoted by NWIA We apply a fuzzy weightedspacing quantity on the FN Then we acquire the intervalapproximations for FN [26]

function is as 119891 = (119891 119891) ([0 1] [0 1]) rarr (RR) andfunctions119891119891 are not negative are uniformly increasing andsatiate the undernormalization term

int

1

0

119891 (119886) 119889119886 = int

1

0

119891 (119886) 119889119886 = 1 (4)

Now let be a fuzzy number with 119860120572= [119886(120572) 119886(120572)] and let

119891(120572) = (119891(120572) 119891(120572)) be aweighted functionThen the interval

NWIA119891(119860) = [int

1

0

119891 (119886) 119886 (119886) 119889119886 int

1

0

119891 (119886) 119886 (119886) 119889119886] (5)

is NWIA to FN In usage the function 119891(120572) may be selected pursuant to

the real termIf = (119886 119887 119888) which is a triangular FN and 119891(120572) =

(119899120572119899minus1 119899120572119899minus1) which is a weighting function so

NWIA119891(119860) = [

119886 + 119899119887

119899 + 1

119899119887 + 119888

119899 + 1

] (6)

Example 1 In this example = (3 4 7) is a triangularFN also 119891

1(120572) = (2120572 2120572) and 119891

2(120572) = (4120572

3 41205723) are two

weighting functionsThen the nearest weighted interval to is as follows (Figure 2) [26]

NWIA1198911(119860) = [

11

3

5]

NWIA1198912(119860) = [

19

5

23

5

]

(7)

34 Goal Programming (GP) The GP attempts to combineoptimal logic and the preference of decision-maker in arith-metical programming in order to satiate several goals Thedecision-making environment determines basic conceptsincluding goal and system restrictions and aim functionvariablesThismeans that GP presents the way for concurrentgoal attainment [27]

Weighted GP is a capable tool since it includes severalfactors simultaneously in the decision-making process and

1

7530

A

11

3

195

235

NWIAf2 NWIAf1

Figure 2 Triangular FN and its interval approximation

at the same time regards the systemrsquos restriction Of courseusing nonquantitative and intangible factors or criteria is outof the capability of this planning model Therefore mix AHPand a supplementary tool capable of solving the shortcomingsof weighted goal planning can shape a suitable model fororganization decision-making such as optimizing the resultmixture

Regard the following problem

Max 1198911(119909) 119891

119896(119909)

st 119909 isin 119883

(8)

where 1198911 119891

119896are goal functions and 119883 is not empty in

an achievable region Model (4) is now a significant areaof MCDM mathematical programming The conception ofgoal programming is to set up an aim level of gainingeach indicator This procedure needs the decision-maker toconsider a goal for each aim that someone wishes to obtainA favored result is then explained as the one which reducesthe deflections from set objectives to the smallest possibleamount After that the GP may be presented as

min119896

sum

119894=1

(119889+

119894+ 119889minus

119894)

st 119891119894(119909) + 119889

+

119894minus 119889minus

119894= 119887119894 119894 = 1 119896

119909 isin 119883

119889+

119894119889minus

119894= 0 119894 = 1 119896

119889+

119894 119889minus

119894ge 0 119894 = 1 119896

(9)

The decision-makers in their objectives set some acceptivedream levels for these objectives and attempt to obtain acollection of objectives as intimately as feasible The aimof programming is to reduce the perversions between theattainment of objectives 119891

119894(119909) and these acceptive dream

levels 119887119894(119894 = 1 119896) In addition119889+

119894and119889minus119894are up anddown

attainment of the 119868th objective respectively

35 Deriving the Weights of Criteria In the routine situationwhenever a matrix 119860 is reciprocal and consistent afterwardsthe weights of criteria are computed as

4 Advances in Materials Science and Engineering

119882119894=

119886119894119895

sum119899

119896=1119886119896119895

119894 = 1 119899 (10)

In the situation of inconsistence matrix we shouldachieve the significance weights or equally 120572

119894119895119908119895minus 119908119894= 0

Hence in the situation of ambiguity for deriving the weightsfrom inconsistence fuzzy matrix we do as [26]

Step 1 First by (8) we convert each fuzzy component 119894119895=

(120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) of the comparison matrix to NWIA 120572

119894119895=

[120572minus119871

119894119895 120572minus119880

119894119895] Therefore the fuzzy comparison matrix is

transformed to an interval matrix 119860

Therefore we present deviation variables 119901minus119894119895 119901+119894119895and 119902minus

119894119895

119902+

119894119895 which lead to

119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

119908119894minus 119886minus119880

119894119895119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

(11)

where deviation variables 119901minus119894119895 119901+119894119895and 119902minus119894119895 119902+119894119895are not negative

real numbers but may not be positive concurrently which is119901minus

119894119895119901+

119894119895= 0 and 119902minus

119894119895119902+

119894119895= 0 Now we use the GP procedure It is

worthwhile that the deviation variables 119901minus119894119895and 119901+

119894119895remain to

be as little as possible which drive to the following GPmodel[26]

min119899

sum

119894=1

119899

sum

119895=1

(119901minus

119894119895+ 119901+

119894119895) 119894 = 1 119899

st 119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0 119894 119895 = 1 119899

119908119894minus 119886minus119880

119894119895119908119894+ 119902minus

119894119895minus 119902+

119894119895= 0 119894 119895 = 1 119899

119899

sum

119894=1

119908119894= 1

119908119894 119901minus

119894119895 119901+

119894119895 119902minus

119894119895 119902+

119894119895ge 0

(12)

By the resolvent model (12) we acquire the optimal weightvector 119882 = (119908

1 119908

119899) and display the significance of

each indicator We can use these weights in the course ofsolving amultiple criteria decision-making problem To solvethis problem we apply the linear programming software11987111986811987311986611987411

Example 2 (matrix with triangular fuzzy number) Regard 3times3 reciprocal matrix with FN

=(

(

1 1 1 2 3 4 4 5 6

1

4

1

3

1

2

1 1 1 3 4 5

1

6

1

5

1

4

1

5

1

4

1

3

1 1 1

)

)

(13)

We apply the function 1198911(120572) = (2120572 2120572) Afterwards by

applying equality (7) the interval approximation pairwisecomparison matrix is acquired as

= (

[1000 1000] [2667 3333] [4667 5333]

[0303 0387] [1000 1000] [3667 4333]

[0192 0217] [0233 0278] [1000 1000]

)

(14)

We build the GP procedure for the mentioned intervalapproximation matrix as

Min = 11990112119897+ 11990112119906+ 11990212119897+ 11990212119906+ 11990113119897+ 11990113119906+ 11990213119897

+ 11990213119906+ 11990121119897+ 11990121119906+ 11990221119897+ 11990221119906+ 11990123119897+ 11990123119906

+ 11990223119897+ 11990223119906+ 11990131119897+ 11990131119906+ 11990231119897+ 11990231119906+ 11990132119897

+ 11990132119906+ 11990232119897+ 11990232119906

2365 lowast 1199082minus 1199081+ 11990112119897minus 11990112119906

= 0

1199081minus 2958 lowast 119908

2+ 11990212119897minus 11990212119906

= 0

1099 lowast 1199082minus 1199081+ 11990113119897minus 11990113119906

= 0

1199081minus 1367 lowast 119908

2+ 11990213119897minus 11990213119906

= 0

0320 lowast 1199081minus 1199082+ 11990121119897minus 11990121119906

= 0

1199082minus 0418 lowast 119908

1+ 11990221119897minus 11990221119906

= 0

2713 lowast 1199083minus 1199082+ 11990123119897minus 11990123119906

= 0

1199082minus 3512 lowast 119908

3+ 11990223119897minus 11990223119906

= 0

0763 lowast 1199081minus 1199083+ 11990131119897minus 11990131119906

= 0

1199083minus 0928 lowast 119908

1+ 11990231119897minus 11990231119906

= 0

0303 lowast 1199082minus 1199083+ 11990132119897minus 11990132119906

= 0

1199083minus 0367 lowast 119908

2+ 11990232119897minus 11990232119906

= 0

1199081+ 1199082+ 1199083= 1

END

(15)

By solving GP (15) we achieve the optimal vector 119882 =

(063 026 009) We may apply these weights in the processof solving a MCDM problem In addition these weightsdisplay that indicator 1 is more significant than others (seeTable 1) In this case the grade arrangement of these indicatorsis as follows

1198821gt 1198822gt 1198823 (16)

The results of ranking these criteria are presented in Table 1

36 FAHP Method The AHP approach applies multicriteriadecision analysis developed 119887 presented by Saaty [28] tocompute the weighting factor of attribute The AHP methodis constructed on the pairwise comparison to compute the

Advances in Materials Science and Engineering 5

Table 1 The result of ranking of proposed method

Criterion Weight Rank1 119882

1= 06334 1

2 1198822= 02678 2

3 1198823= 00987 3

Alternative 2Alternative 1 Alternative 3

Criterion 2 Criterion 3Criterion 1

Goal

Figure 3 A hierarchical structure

weight of each criterion The AHP permits experts to deter-mine the significance of each criterion during comparingother criteria from 1 to 9 from ldquosame importancerdquo (1)to ldquocompletely more importantrdquo (9) Building a decisiontree decision-maker is permitted to first describe weightsof the main criteria and then decision-maker can describethe lower level subcriteria that exactly describe the testedmulticriteria issue [28]

The AHP method may not handle the ambiguity indetermining the rankings of various attributes [29] Alsoit is usually hard to evaluate various factors because of alack of suitable data In FAHP method quid pro quo ofallocating definite quantities the adjudications are built byapplying linguistic parameters and are characterized by fuzzymembership functionsThe fuzzy geometric mean method isthe most accepted method to construct the matrix The relictprocedures are just routine AHP

37 Proposed Algorithm An algorithm to determine themostpreferable aluminum waste management system selectionamong all possible alternatives when data is fuzzy by usingGP and the NWIA with the extended AHP method is givenin the following

Step 1 (set up the expert group) To evaluate alternatives anexpert group comprised of researcher and managers shouldbe formed

Step 2 Create a hierarchical structure of elements for prob-lem solving For this propose it is necessary for decision-makers to determine criteria and subcriteria based onproposing the main target See for example Figure 3

Step 3 Build a set of fuzzy comparison matrices for eachdecision-maker

Step 4 (aggregate fuzzy comparison matrices) We aggregatefuzzy comparison matrices constructed by decision-makers

by using the geometric mean method and convert them tounit fuzzy comparison matrix

where 119886119871119894119895= (

5

prod

119896=1

119886119871119896

119894119895)

15

119886119872

119894119895= (

5

prod

119896=1

119886119872119870

119894119895)

15

119886119880

119894119895= (

5

prod

119896=1

119886119880119870

119894119895)

15

(119886119871119896

119894119895 119886119872119870

119894119895 119886119880119870

119894119895) 119896 = 1 2 5

(17)

is the important opinion of the119870th decision-maker

Step 5 (deriving theweights of eachmatrix) For this purposewe apply the following substeps

Step 51 By using (7) we convert each fuzzy matrix to aninterval fuzzy matrix

Step 52 By resolving model (12) we can achieve the weightof each comparison matrix

Step 6 (aggregate the weights and rank the alternatives) Weaggregate the weights and rank the alternatives and finallyselect the best aluminum waste management system Thepriorityweight of each optionmay be achieved bymultiplyingthe matrix of assessment by the vector of characteristicweights and adding over all characteristics [30]

4 Case Study

A case study on aluminum manufacturers and particularlyaluminum remelter plants in Arak an industrial city in Iranis introduced It illustrates how the proposed fuzzy AHPmethodology according to the algorithm can be applied toselecting the best aluminum waste management system

Twenty-nine remelting facilities were incorporated in thisresearch The secondary aluminum remelting is consideredas a unit function As shown in Figure 4 this process unitincludes the storage in place (1) beneficiation activities (2)related to input aluminum scrap such as washing separatingand sorting (orwithout beneficiation activities (3)) remeltingin the crucible furnace (4) duplicate aluminum black drossrecycling in plant (5) (or exporting aluminum black drossto another place and duplicate recycling (6)) and final wastelandfilling (7) (or release in the environment (8))

All the results are based on the reference flow of 1 tonof aluminum batch including new and old aluminum scrapsand white and black aluminum dross (see Figure 5) Theupkeep and repair of the plant and equipment materialsare provided to this life cycle stage from both primaryand secondary aluminum processing Also the secondaryremelters have a diversity of melting furnaces top-loadedclosed rotary and side well-feeding melting They have

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

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MaterialsJournal of

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Nano

materials

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Journal ofNanomaterials

2 Advances in Materials Science and Engineering

2 Literature Review

Total primary aluminum consumption in the world was of502Mt in 2013 [2] The manufacture of aluminum fromalumina demands much more energy than other metals andleads to major quantities of greenhouse gas pollutants [3]Aluminum production is responsible for 11 of the annualgreenhouse gas emissions [4] It is about 75 of all thealuminum production as secondary aluminum (aluminumscrap and dross) since 1880s which is still in generative useThe findings of these studies indicated that the emissions andenergy consumption of aluminumwere decreased in the pro-duction of secondary aluminum compared to the productionof primary aluminum [5] Authors represented that the alu-minum waste recycling is economically and environmentallyfriendly [6] Opportunities for recovery and recycle of metalsfrom wastes are high Recovery of secondary resources suchas Al Fe Cu and Zn from these wastes is gaining increasinginterest [7 8] Also by recycling secondary aluminumresources are saved the need for landfill area could have beendecreased and the public opinion would be satisfied A lotof dross is produced as a waste product during remeltingor refining aluminum [9] Although aluminum dross is awaste of current resources in case of being landfilled withoutsuitable treatment it will lead to the secondary contaminantswhich would affect air water and soil [1] Aluminum wastesmainly are disposed of in landfill sites which may resultin leaking of toxic metal ions into the ground water Alsowhen aluminum waste comes in contact with water it emitspoisonous gases as NH

3 CH4 PH3 H2 and H

2S [10 11]

The environmental effects of aluminum scrap from recycledaluminum should beminimizedThat iswhy in this study theeffects and impacts of aluminum waste management systemsare evaluated In addition aluminumdross recycling has beenalways considered as a problematic issue The fuzzy set ideawas used by [12] to manage uncertainty in the inventorydata Seppala modified and compared the fuzzy approachpresented in [13] to the ldquotraditionalrdquo valuation method ofLCA [14] Since Van Laarhoven Pedrycz and Buckley [1516] offered their initial study in FAHP numerous workshave applied FAHP in disparate environment problems [17ndash20] Also some studies applied FAHP method concerningLCA thinking For example this methodology was appliedby Zheng et al in the building sector [21] and by Chanand Lin to evaluate green product design [19 22] Complexdecision-making situations are relevant to the aluminumwaste management system which needs the realization ofdifferent sections of the industry and community Howeverlittle attention has been given to the environmental aspectsof the processing output of aluminum dross and aluminumscrap as aluminum waste in MCDMmethodologies

3 Methodology

The aim of this work is to offer a methodical and straight-forward and simple to use method for the aluminum wastemanagement system selection problem MCDM methodswere considered for this aim including fuzzy logic fuzzycomparison matrix NWIA the GP method and the fuzzyAHP

cba0

1

Figure 1 Typical triangular fuzzy number

31 Fuzzy Numbers (FN) FN are one path to explain theambiguity and be missing accuracy of data [23] A fuzzynumber is a fuzzy set 119860 119877 rarr 119868 = [0 1]119877 that satisfiedthe following

(1) ldquo119860rdquo is continuous

(2) 119860(119909) = 0 outside some interval [119886 119888]

(3) There are real numbers 119886 119887 and 119888 so that 119886 le 119887 le 119888

And

(a) 119860(119909) = 1 119909 = 119887(b) 119860(119909) is decreasing on [119887 119888](c) 119860(119909) is increasing on 119886 le 119909 le 119887

The set of all such fuzzy numbers is represented by 119865(R)Fuzzy numberwith linear sides and themembership functionhaving the following form (see Figure 1)

119860 (119883) =

119909 minus 119886

119887 minus 119886

119886 le 119909 le 119887

119888 minus 119909

119888 minus 119887

119887 le 119909 le 119888

0 otherwise

(1)

is called triangular fuzzy number and is denoted by =

(119886 119887 119888)

32 Fuzzy Pair Comparison Matrix Consider the expert thatprepares fuzzy opinion in place of exact opinion It presumestrade to be with comparison matrix with triangular FN beingthe components of the matrix We suppose a matrix whosecomponents are FN as

= (

(119886119871

11 119886119872

11 119886119880

11) sdot sdot sdot (119886

119871

1119899 119886119872

1119899 119886119880

1119899)

d

(119886119871

1198991 119886119872

1198991 119886119880

119899119899) sdot sdot sdot (119886

119871

119899119899 119886119872

119899119899 119886119880

119899119899)

) (2)

Advances in Materials Science and Engineering 3

where = (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) is a triangular FN see [24] It is

supposed that is reciprocal if the following term is satisfied[25]

119894119895= (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) forall119894 119895 = 1 119899

implies that 119894119895= (

1

1205721198801015840

119894119895

1

1205721198721015840

119894119895

1

1205721198711015840

119894119895

)

forall119894 119895 = 1 119899

(3)

33 The Nearest Weighted Interval Approximations (NWIAs)In this section we review an interval processor of FNwhich is denoted by NWIA We apply a fuzzy weightedspacing quantity on the FN Then we acquire the intervalapproximations for FN [26]

function is as 119891 = (119891 119891) ([0 1] [0 1]) rarr (RR) andfunctions119891119891 are not negative are uniformly increasing andsatiate the undernormalization term

int

1

0

119891 (119886) 119889119886 = int

1

0

119891 (119886) 119889119886 = 1 (4)

Now let be a fuzzy number with 119860120572= [119886(120572) 119886(120572)] and let

119891(120572) = (119891(120572) 119891(120572)) be aweighted functionThen the interval

NWIA119891(119860) = [int

1

0

119891 (119886) 119886 (119886) 119889119886 int

1

0

119891 (119886) 119886 (119886) 119889119886] (5)

is NWIA to FN In usage the function 119891(120572) may be selected pursuant to

the real termIf = (119886 119887 119888) which is a triangular FN and 119891(120572) =

(119899120572119899minus1 119899120572119899minus1) which is a weighting function so

NWIA119891(119860) = [

119886 + 119899119887

119899 + 1

119899119887 + 119888

119899 + 1

] (6)

Example 1 In this example = (3 4 7) is a triangularFN also 119891

1(120572) = (2120572 2120572) and 119891

2(120572) = (4120572

3 41205723) are two

weighting functionsThen the nearest weighted interval to is as follows (Figure 2) [26]

NWIA1198911(119860) = [

11

3

5]

NWIA1198912(119860) = [

19

5

23

5

]

(7)

34 Goal Programming (GP) The GP attempts to combineoptimal logic and the preference of decision-maker in arith-metical programming in order to satiate several goals Thedecision-making environment determines basic conceptsincluding goal and system restrictions and aim functionvariablesThismeans that GP presents the way for concurrentgoal attainment [27]

Weighted GP is a capable tool since it includes severalfactors simultaneously in the decision-making process and

1

7530

A

11

3

195

235

NWIAf2 NWIAf1

Figure 2 Triangular FN and its interval approximation

at the same time regards the systemrsquos restriction Of courseusing nonquantitative and intangible factors or criteria is outof the capability of this planning model Therefore mix AHPand a supplementary tool capable of solving the shortcomingsof weighted goal planning can shape a suitable model fororganization decision-making such as optimizing the resultmixture

Regard the following problem

Max 1198911(119909) 119891

119896(119909)

st 119909 isin 119883

(8)

where 1198911 119891

119896are goal functions and 119883 is not empty in

an achievable region Model (4) is now a significant areaof MCDM mathematical programming The conception ofgoal programming is to set up an aim level of gainingeach indicator This procedure needs the decision-maker toconsider a goal for each aim that someone wishes to obtainA favored result is then explained as the one which reducesthe deflections from set objectives to the smallest possibleamount After that the GP may be presented as

min119896

sum

119894=1

(119889+

119894+ 119889minus

119894)

st 119891119894(119909) + 119889

+

119894minus 119889minus

119894= 119887119894 119894 = 1 119896

119909 isin 119883

119889+

119894119889minus

119894= 0 119894 = 1 119896

119889+

119894 119889minus

119894ge 0 119894 = 1 119896

(9)

The decision-makers in their objectives set some acceptivedream levels for these objectives and attempt to obtain acollection of objectives as intimately as feasible The aimof programming is to reduce the perversions between theattainment of objectives 119891

119894(119909) and these acceptive dream

levels 119887119894(119894 = 1 119896) In addition119889+

119894and119889minus119894are up anddown

attainment of the 119868th objective respectively

35 Deriving the Weights of Criteria In the routine situationwhenever a matrix 119860 is reciprocal and consistent afterwardsthe weights of criteria are computed as

4 Advances in Materials Science and Engineering

119882119894=

119886119894119895

sum119899

119896=1119886119896119895

119894 = 1 119899 (10)

In the situation of inconsistence matrix we shouldachieve the significance weights or equally 120572

119894119895119908119895minus 119908119894= 0

Hence in the situation of ambiguity for deriving the weightsfrom inconsistence fuzzy matrix we do as [26]

Step 1 First by (8) we convert each fuzzy component 119894119895=

(120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) of the comparison matrix to NWIA 120572

119894119895=

[120572minus119871

119894119895 120572minus119880

119894119895] Therefore the fuzzy comparison matrix is

transformed to an interval matrix 119860

Therefore we present deviation variables 119901minus119894119895 119901+119894119895and 119902minus

119894119895

119902+

119894119895 which lead to

119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

119908119894minus 119886minus119880

119894119895119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

(11)

where deviation variables 119901minus119894119895 119901+119894119895and 119902minus119894119895 119902+119894119895are not negative

real numbers but may not be positive concurrently which is119901minus

119894119895119901+

119894119895= 0 and 119902minus

119894119895119902+

119894119895= 0 Now we use the GP procedure It is

worthwhile that the deviation variables 119901minus119894119895and 119901+

119894119895remain to

be as little as possible which drive to the following GPmodel[26]

min119899

sum

119894=1

119899

sum

119895=1

(119901minus

119894119895+ 119901+

119894119895) 119894 = 1 119899

st 119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0 119894 119895 = 1 119899

119908119894minus 119886minus119880

119894119895119908119894+ 119902minus

119894119895minus 119902+

119894119895= 0 119894 119895 = 1 119899

119899

sum

119894=1

119908119894= 1

119908119894 119901minus

119894119895 119901+

119894119895 119902minus

119894119895 119902+

119894119895ge 0

(12)

By the resolvent model (12) we acquire the optimal weightvector 119882 = (119908

1 119908

119899) and display the significance of

each indicator We can use these weights in the course ofsolving amultiple criteria decision-making problem To solvethis problem we apply the linear programming software11987111986811987311986611987411

Example 2 (matrix with triangular fuzzy number) Regard 3times3 reciprocal matrix with FN

=(

(

1 1 1 2 3 4 4 5 6

1

4

1

3

1

2

1 1 1 3 4 5

1

6

1

5

1

4

1

5

1

4

1

3

1 1 1

)

)

(13)

We apply the function 1198911(120572) = (2120572 2120572) Afterwards by

applying equality (7) the interval approximation pairwisecomparison matrix is acquired as

= (

[1000 1000] [2667 3333] [4667 5333]

[0303 0387] [1000 1000] [3667 4333]

[0192 0217] [0233 0278] [1000 1000]

)

(14)

We build the GP procedure for the mentioned intervalapproximation matrix as

Min = 11990112119897+ 11990112119906+ 11990212119897+ 11990212119906+ 11990113119897+ 11990113119906+ 11990213119897

+ 11990213119906+ 11990121119897+ 11990121119906+ 11990221119897+ 11990221119906+ 11990123119897+ 11990123119906

+ 11990223119897+ 11990223119906+ 11990131119897+ 11990131119906+ 11990231119897+ 11990231119906+ 11990132119897

+ 11990132119906+ 11990232119897+ 11990232119906

2365 lowast 1199082minus 1199081+ 11990112119897minus 11990112119906

= 0

1199081minus 2958 lowast 119908

2+ 11990212119897minus 11990212119906

= 0

1099 lowast 1199082minus 1199081+ 11990113119897minus 11990113119906

= 0

1199081minus 1367 lowast 119908

2+ 11990213119897minus 11990213119906

= 0

0320 lowast 1199081minus 1199082+ 11990121119897minus 11990121119906

= 0

1199082minus 0418 lowast 119908

1+ 11990221119897minus 11990221119906

= 0

2713 lowast 1199083minus 1199082+ 11990123119897minus 11990123119906

= 0

1199082minus 3512 lowast 119908

3+ 11990223119897minus 11990223119906

= 0

0763 lowast 1199081minus 1199083+ 11990131119897minus 11990131119906

= 0

1199083minus 0928 lowast 119908

1+ 11990231119897minus 11990231119906

= 0

0303 lowast 1199082minus 1199083+ 11990132119897minus 11990132119906

= 0

1199083minus 0367 lowast 119908

2+ 11990232119897minus 11990232119906

= 0

1199081+ 1199082+ 1199083= 1

END

(15)

By solving GP (15) we achieve the optimal vector 119882 =

(063 026 009) We may apply these weights in the processof solving a MCDM problem In addition these weightsdisplay that indicator 1 is more significant than others (seeTable 1) In this case the grade arrangement of these indicatorsis as follows

1198821gt 1198822gt 1198823 (16)

The results of ranking these criteria are presented in Table 1

36 FAHP Method The AHP approach applies multicriteriadecision analysis developed 119887 presented by Saaty [28] tocompute the weighting factor of attribute The AHP methodis constructed on the pairwise comparison to compute the

Advances in Materials Science and Engineering 5

Table 1 The result of ranking of proposed method

Criterion Weight Rank1 119882

1= 06334 1

2 1198822= 02678 2

3 1198823= 00987 3

Alternative 2Alternative 1 Alternative 3

Criterion 2 Criterion 3Criterion 1

Goal

Figure 3 A hierarchical structure

weight of each criterion The AHP permits experts to deter-mine the significance of each criterion during comparingother criteria from 1 to 9 from ldquosame importancerdquo (1)to ldquocompletely more importantrdquo (9) Building a decisiontree decision-maker is permitted to first describe weightsof the main criteria and then decision-maker can describethe lower level subcriteria that exactly describe the testedmulticriteria issue [28]

The AHP method may not handle the ambiguity indetermining the rankings of various attributes [29] Alsoit is usually hard to evaluate various factors because of alack of suitable data In FAHP method quid pro quo ofallocating definite quantities the adjudications are built byapplying linguistic parameters and are characterized by fuzzymembership functionsThe fuzzy geometric mean method isthe most accepted method to construct the matrix The relictprocedures are just routine AHP

37 Proposed Algorithm An algorithm to determine themostpreferable aluminum waste management system selectionamong all possible alternatives when data is fuzzy by usingGP and the NWIA with the extended AHP method is givenin the following

Step 1 (set up the expert group) To evaluate alternatives anexpert group comprised of researcher and managers shouldbe formed

Step 2 Create a hierarchical structure of elements for prob-lem solving For this propose it is necessary for decision-makers to determine criteria and subcriteria based onproposing the main target See for example Figure 3

Step 3 Build a set of fuzzy comparison matrices for eachdecision-maker

Step 4 (aggregate fuzzy comparison matrices) We aggregatefuzzy comparison matrices constructed by decision-makers

by using the geometric mean method and convert them tounit fuzzy comparison matrix

where 119886119871119894119895= (

5

prod

119896=1

119886119871119896

119894119895)

15

119886119872

119894119895= (

5

prod

119896=1

119886119872119870

119894119895)

15

119886119880

119894119895= (

5

prod

119896=1

119886119880119870

119894119895)

15

(119886119871119896

119894119895 119886119872119870

119894119895 119886119880119870

119894119895) 119896 = 1 2 5

(17)

is the important opinion of the119870th decision-maker

Step 5 (deriving theweights of eachmatrix) For this purposewe apply the following substeps

Step 51 By using (7) we convert each fuzzy matrix to aninterval fuzzy matrix

Step 52 By resolving model (12) we can achieve the weightof each comparison matrix

Step 6 (aggregate the weights and rank the alternatives) Weaggregate the weights and rank the alternatives and finallyselect the best aluminum waste management system Thepriorityweight of each optionmay be achieved bymultiplyingthe matrix of assessment by the vector of characteristicweights and adding over all characteristics [30]

4 Case Study

A case study on aluminum manufacturers and particularlyaluminum remelter plants in Arak an industrial city in Iranis introduced It illustrates how the proposed fuzzy AHPmethodology according to the algorithm can be applied toselecting the best aluminum waste management system

Twenty-nine remelting facilities were incorporated in thisresearch The secondary aluminum remelting is consideredas a unit function As shown in Figure 4 this process unitincludes the storage in place (1) beneficiation activities (2)related to input aluminum scrap such as washing separatingand sorting (orwithout beneficiation activities (3)) remeltingin the crucible furnace (4) duplicate aluminum black drossrecycling in plant (5) (or exporting aluminum black drossto another place and duplicate recycling (6)) and final wastelandfilling (7) (or release in the environment (8))

All the results are based on the reference flow of 1 tonof aluminum batch including new and old aluminum scrapsand white and black aluminum dross (see Figure 5) Theupkeep and repair of the plant and equipment materialsare provided to this life cycle stage from both primaryand secondary aluminum processing Also the secondaryremelters have a diversity of melting furnaces top-loadedclosed rotary and side well-feeding melting They have

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Biomaterials

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

where = (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) is a triangular FN see [24] It is

supposed that is reciprocal if the following term is satisfied[25]

119894119895= (120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) forall119894 119895 = 1 119899

implies that 119894119895= (

1

1205721198801015840

119894119895

1

1205721198721015840

119894119895

1

1205721198711015840

119894119895

)

forall119894 119895 = 1 119899

(3)

33 The Nearest Weighted Interval Approximations (NWIAs)In this section we review an interval processor of FNwhich is denoted by NWIA We apply a fuzzy weightedspacing quantity on the FN Then we acquire the intervalapproximations for FN [26]

function is as 119891 = (119891 119891) ([0 1] [0 1]) rarr (RR) andfunctions119891119891 are not negative are uniformly increasing andsatiate the undernormalization term

int

1

0

119891 (119886) 119889119886 = int

1

0

119891 (119886) 119889119886 = 1 (4)

Now let be a fuzzy number with 119860120572= [119886(120572) 119886(120572)] and let

119891(120572) = (119891(120572) 119891(120572)) be aweighted functionThen the interval

NWIA119891(119860) = [int

1

0

119891 (119886) 119886 (119886) 119889119886 int

1

0

119891 (119886) 119886 (119886) 119889119886] (5)

is NWIA to FN In usage the function 119891(120572) may be selected pursuant to

the real termIf = (119886 119887 119888) which is a triangular FN and 119891(120572) =

(119899120572119899minus1 119899120572119899minus1) which is a weighting function so

NWIA119891(119860) = [

119886 + 119899119887

119899 + 1

119899119887 + 119888

119899 + 1

] (6)

Example 1 In this example = (3 4 7) is a triangularFN also 119891

1(120572) = (2120572 2120572) and 119891

2(120572) = (4120572

3 41205723) are two

weighting functionsThen the nearest weighted interval to is as follows (Figure 2) [26]

NWIA1198911(119860) = [

11

3

5]

NWIA1198912(119860) = [

19

5

23

5

]

(7)

34 Goal Programming (GP) The GP attempts to combineoptimal logic and the preference of decision-maker in arith-metical programming in order to satiate several goals Thedecision-making environment determines basic conceptsincluding goal and system restrictions and aim functionvariablesThismeans that GP presents the way for concurrentgoal attainment [27]

Weighted GP is a capable tool since it includes severalfactors simultaneously in the decision-making process and

1

7530

A

11

3

195

235

NWIAf2 NWIAf1

Figure 2 Triangular FN and its interval approximation

at the same time regards the systemrsquos restriction Of courseusing nonquantitative and intangible factors or criteria is outof the capability of this planning model Therefore mix AHPand a supplementary tool capable of solving the shortcomingsof weighted goal planning can shape a suitable model fororganization decision-making such as optimizing the resultmixture

Regard the following problem

Max 1198911(119909) 119891

119896(119909)

st 119909 isin 119883

(8)

where 1198911 119891

119896are goal functions and 119883 is not empty in

an achievable region Model (4) is now a significant areaof MCDM mathematical programming The conception ofgoal programming is to set up an aim level of gainingeach indicator This procedure needs the decision-maker toconsider a goal for each aim that someone wishes to obtainA favored result is then explained as the one which reducesthe deflections from set objectives to the smallest possibleamount After that the GP may be presented as

min119896

sum

119894=1

(119889+

119894+ 119889minus

119894)

st 119891119894(119909) + 119889

+

119894minus 119889minus

119894= 119887119894 119894 = 1 119896

119909 isin 119883

119889+

119894119889minus

119894= 0 119894 = 1 119896

119889+

119894 119889minus

119894ge 0 119894 = 1 119896

(9)

The decision-makers in their objectives set some acceptivedream levels for these objectives and attempt to obtain acollection of objectives as intimately as feasible The aimof programming is to reduce the perversions between theattainment of objectives 119891

119894(119909) and these acceptive dream

levels 119887119894(119894 = 1 119896) In addition119889+

119894and119889minus119894are up anddown

attainment of the 119868th objective respectively

35 Deriving the Weights of Criteria In the routine situationwhenever a matrix 119860 is reciprocal and consistent afterwardsthe weights of criteria are computed as

4 Advances in Materials Science and Engineering

119882119894=

119886119894119895

sum119899

119896=1119886119896119895

119894 = 1 119899 (10)

In the situation of inconsistence matrix we shouldachieve the significance weights or equally 120572

119894119895119908119895minus 119908119894= 0

Hence in the situation of ambiguity for deriving the weightsfrom inconsistence fuzzy matrix we do as [26]

Step 1 First by (8) we convert each fuzzy component 119894119895=

(120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) of the comparison matrix to NWIA 120572

119894119895=

[120572minus119871

119894119895 120572minus119880

119894119895] Therefore the fuzzy comparison matrix is

transformed to an interval matrix 119860

Therefore we present deviation variables 119901minus119894119895 119901+119894119895and 119902minus

119894119895

119902+

119894119895 which lead to

119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

119908119894minus 119886minus119880

119894119895119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

(11)

where deviation variables 119901minus119894119895 119901+119894119895and 119902minus119894119895 119902+119894119895are not negative

real numbers but may not be positive concurrently which is119901minus

119894119895119901+

119894119895= 0 and 119902minus

119894119895119902+

119894119895= 0 Now we use the GP procedure It is

worthwhile that the deviation variables 119901minus119894119895and 119901+

119894119895remain to

be as little as possible which drive to the following GPmodel[26]

min119899

sum

119894=1

119899

sum

119895=1

(119901minus

119894119895+ 119901+

119894119895) 119894 = 1 119899

st 119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0 119894 119895 = 1 119899

119908119894minus 119886minus119880

119894119895119908119894+ 119902minus

119894119895minus 119902+

119894119895= 0 119894 119895 = 1 119899

119899

sum

119894=1

119908119894= 1

119908119894 119901minus

119894119895 119901+

119894119895 119902minus

119894119895 119902+

119894119895ge 0

(12)

By the resolvent model (12) we acquire the optimal weightvector 119882 = (119908

1 119908

119899) and display the significance of

each indicator We can use these weights in the course ofsolving amultiple criteria decision-making problem To solvethis problem we apply the linear programming software11987111986811987311986611987411

Example 2 (matrix with triangular fuzzy number) Regard 3times3 reciprocal matrix with FN

=(

(

1 1 1 2 3 4 4 5 6

1

4

1

3

1

2

1 1 1 3 4 5

1

6

1

5

1

4

1

5

1

4

1

3

1 1 1

)

)

(13)

We apply the function 1198911(120572) = (2120572 2120572) Afterwards by

applying equality (7) the interval approximation pairwisecomparison matrix is acquired as

= (

[1000 1000] [2667 3333] [4667 5333]

[0303 0387] [1000 1000] [3667 4333]

[0192 0217] [0233 0278] [1000 1000]

)

(14)

We build the GP procedure for the mentioned intervalapproximation matrix as

Min = 11990112119897+ 11990112119906+ 11990212119897+ 11990212119906+ 11990113119897+ 11990113119906+ 11990213119897

+ 11990213119906+ 11990121119897+ 11990121119906+ 11990221119897+ 11990221119906+ 11990123119897+ 11990123119906

+ 11990223119897+ 11990223119906+ 11990131119897+ 11990131119906+ 11990231119897+ 11990231119906+ 11990132119897

+ 11990132119906+ 11990232119897+ 11990232119906

2365 lowast 1199082minus 1199081+ 11990112119897minus 11990112119906

= 0

1199081minus 2958 lowast 119908

2+ 11990212119897minus 11990212119906

= 0

1099 lowast 1199082minus 1199081+ 11990113119897minus 11990113119906

= 0

1199081minus 1367 lowast 119908

2+ 11990213119897minus 11990213119906

= 0

0320 lowast 1199081minus 1199082+ 11990121119897minus 11990121119906

= 0

1199082minus 0418 lowast 119908

1+ 11990221119897minus 11990221119906

= 0

2713 lowast 1199083minus 1199082+ 11990123119897minus 11990123119906

= 0

1199082minus 3512 lowast 119908

3+ 11990223119897minus 11990223119906

= 0

0763 lowast 1199081minus 1199083+ 11990131119897minus 11990131119906

= 0

1199083minus 0928 lowast 119908

1+ 11990231119897minus 11990231119906

= 0

0303 lowast 1199082minus 1199083+ 11990132119897minus 11990132119906

= 0

1199083minus 0367 lowast 119908

2+ 11990232119897minus 11990232119906

= 0

1199081+ 1199082+ 1199083= 1

END

(15)

By solving GP (15) we achieve the optimal vector 119882 =

(063 026 009) We may apply these weights in the processof solving a MCDM problem In addition these weightsdisplay that indicator 1 is more significant than others (seeTable 1) In this case the grade arrangement of these indicatorsis as follows

1198821gt 1198822gt 1198823 (16)

The results of ranking these criteria are presented in Table 1

36 FAHP Method The AHP approach applies multicriteriadecision analysis developed 119887 presented by Saaty [28] tocompute the weighting factor of attribute The AHP methodis constructed on the pairwise comparison to compute the

Advances in Materials Science and Engineering 5

Table 1 The result of ranking of proposed method

Criterion Weight Rank1 119882

1= 06334 1

2 1198822= 02678 2

3 1198823= 00987 3

Alternative 2Alternative 1 Alternative 3

Criterion 2 Criterion 3Criterion 1

Goal

Figure 3 A hierarchical structure

weight of each criterion The AHP permits experts to deter-mine the significance of each criterion during comparingother criteria from 1 to 9 from ldquosame importancerdquo (1)to ldquocompletely more importantrdquo (9) Building a decisiontree decision-maker is permitted to first describe weightsof the main criteria and then decision-maker can describethe lower level subcriteria that exactly describe the testedmulticriteria issue [28]

The AHP method may not handle the ambiguity indetermining the rankings of various attributes [29] Alsoit is usually hard to evaluate various factors because of alack of suitable data In FAHP method quid pro quo ofallocating definite quantities the adjudications are built byapplying linguistic parameters and are characterized by fuzzymembership functionsThe fuzzy geometric mean method isthe most accepted method to construct the matrix The relictprocedures are just routine AHP

37 Proposed Algorithm An algorithm to determine themostpreferable aluminum waste management system selectionamong all possible alternatives when data is fuzzy by usingGP and the NWIA with the extended AHP method is givenin the following

Step 1 (set up the expert group) To evaluate alternatives anexpert group comprised of researcher and managers shouldbe formed

Step 2 Create a hierarchical structure of elements for prob-lem solving For this propose it is necessary for decision-makers to determine criteria and subcriteria based onproposing the main target See for example Figure 3

Step 3 Build a set of fuzzy comparison matrices for eachdecision-maker

Step 4 (aggregate fuzzy comparison matrices) We aggregatefuzzy comparison matrices constructed by decision-makers

by using the geometric mean method and convert them tounit fuzzy comparison matrix

where 119886119871119894119895= (

5

prod

119896=1

119886119871119896

119894119895)

15

119886119872

119894119895= (

5

prod

119896=1

119886119872119870

119894119895)

15

119886119880

119894119895= (

5

prod

119896=1

119886119880119870

119894119895)

15

(119886119871119896

119894119895 119886119872119870

119894119895 119886119880119870

119894119895) 119896 = 1 2 5

(17)

is the important opinion of the119870th decision-maker

Step 5 (deriving theweights of eachmatrix) For this purposewe apply the following substeps

Step 51 By using (7) we convert each fuzzy matrix to aninterval fuzzy matrix

Step 52 By resolving model (12) we can achieve the weightof each comparison matrix

Step 6 (aggregate the weights and rank the alternatives) Weaggregate the weights and rank the alternatives and finallyselect the best aluminum waste management system Thepriorityweight of each optionmay be achieved bymultiplyingthe matrix of assessment by the vector of characteristicweights and adding over all characteristics [30]

4 Case Study

A case study on aluminum manufacturers and particularlyaluminum remelter plants in Arak an industrial city in Iranis introduced It illustrates how the proposed fuzzy AHPmethodology according to the algorithm can be applied toselecting the best aluminum waste management system

Twenty-nine remelting facilities were incorporated in thisresearch The secondary aluminum remelting is consideredas a unit function As shown in Figure 4 this process unitincludes the storage in place (1) beneficiation activities (2)related to input aluminum scrap such as washing separatingand sorting (orwithout beneficiation activities (3)) remeltingin the crucible furnace (4) duplicate aluminum black drossrecycling in plant (5) (or exporting aluminum black drossto another place and duplicate recycling (6)) and final wastelandfilling (7) (or release in the environment (8))

All the results are based on the reference flow of 1 tonof aluminum batch including new and old aluminum scrapsand white and black aluminum dross (see Figure 5) Theupkeep and repair of the plant and equipment materialsare provided to this life cycle stage from both primaryand secondary aluminum processing Also the secondaryremelters have a diversity of melting furnaces top-loadedclosed rotary and side well-feeding melting They have

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Nano

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Journal ofNanomaterials

4 Advances in Materials Science and Engineering

119882119894=

119886119894119895

sum119899

119896=1119886119896119895

119894 = 1 119899 (10)

In the situation of inconsistence matrix we shouldachieve the significance weights or equally 120572

119894119895119908119895minus 119908119894= 0

Hence in the situation of ambiguity for deriving the weightsfrom inconsistence fuzzy matrix we do as [26]

Step 1 First by (8) we convert each fuzzy component 119894119895=

(120572119871

119894119895 120572119872

119894119895 120572119880

119894119895) of the comparison matrix to NWIA 120572

119894119895=

[120572minus119871

119894119895 120572minus119880

119894119895] Therefore the fuzzy comparison matrix is

transformed to an interval matrix 119860

Therefore we present deviation variables 119901minus119894119895 119901+119894119895and 119902minus

119894119895

119902+

119894119895 which lead to

119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

119908119894minus 119886minus119880

119894119895119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0

(11)

where deviation variables 119901minus119894119895 119901+119894119895and 119902minus119894119895 119902+119894119895are not negative

real numbers but may not be positive concurrently which is119901minus

119894119895119901+

119894119895= 0 and 119902minus

119894119895119902+

119894119895= 0 Now we use the GP procedure It is

worthwhile that the deviation variables 119901minus119894119895and 119901+

119894119895remain to

be as little as possible which drive to the following GPmodel[26]

min119899

sum

119894=1

119899

sum

119895=1

(119901minus

119894119895+ 119901+

119894119895) 119894 = 1 119899

st 119886minus119871

119894119895119908119894minus 119908119894+ 119901minus

119894119895minus 119901+

119894119895= 0 119894 119895 = 1 119899

119908119894minus 119886minus119880

119894119895119908119894+ 119902minus

119894119895minus 119902+

119894119895= 0 119894 119895 = 1 119899

119899

sum

119894=1

119908119894= 1

119908119894 119901minus

119894119895 119901+

119894119895 119902minus

119894119895 119902+

119894119895ge 0

(12)

By the resolvent model (12) we acquire the optimal weightvector 119882 = (119908

1 119908

119899) and display the significance of

each indicator We can use these weights in the course ofsolving amultiple criteria decision-making problem To solvethis problem we apply the linear programming software11987111986811987311986611987411

Example 2 (matrix with triangular fuzzy number) Regard 3times3 reciprocal matrix with FN

=(

(

1 1 1 2 3 4 4 5 6

1

4

1

3

1

2

1 1 1 3 4 5

1

6

1

5

1

4

1

5

1

4

1

3

1 1 1

)

)

(13)

We apply the function 1198911(120572) = (2120572 2120572) Afterwards by

applying equality (7) the interval approximation pairwisecomparison matrix is acquired as

= (

[1000 1000] [2667 3333] [4667 5333]

[0303 0387] [1000 1000] [3667 4333]

[0192 0217] [0233 0278] [1000 1000]

)

(14)

We build the GP procedure for the mentioned intervalapproximation matrix as

Min = 11990112119897+ 11990112119906+ 11990212119897+ 11990212119906+ 11990113119897+ 11990113119906+ 11990213119897

+ 11990213119906+ 11990121119897+ 11990121119906+ 11990221119897+ 11990221119906+ 11990123119897+ 11990123119906

+ 11990223119897+ 11990223119906+ 11990131119897+ 11990131119906+ 11990231119897+ 11990231119906+ 11990132119897

+ 11990132119906+ 11990232119897+ 11990232119906

2365 lowast 1199082minus 1199081+ 11990112119897minus 11990112119906

= 0

1199081minus 2958 lowast 119908

2+ 11990212119897minus 11990212119906

= 0

1099 lowast 1199082minus 1199081+ 11990113119897minus 11990113119906

= 0

1199081minus 1367 lowast 119908

2+ 11990213119897minus 11990213119906

= 0

0320 lowast 1199081minus 1199082+ 11990121119897minus 11990121119906

= 0

1199082minus 0418 lowast 119908

1+ 11990221119897minus 11990221119906

= 0

2713 lowast 1199083minus 1199082+ 11990123119897minus 11990123119906

= 0

1199082minus 3512 lowast 119908

3+ 11990223119897minus 11990223119906

= 0

0763 lowast 1199081minus 1199083+ 11990131119897minus 11990131119906

= 0

1199083minus 0928 lowast 119908

1+ 11990231119897minus 11990231119906

= 0

0303 lowast 1199082minus 1199083+ 11990132119897minus 11990132119906

= 0

1199083minus 0367 lowast 119908

2+ 11990232119897minus 11990232119906

= 0

1199081+ 1199082+ 1199083= 1

END

(15)

By solving GP (15) we achieve the optimal vector 119882 =

(063 026 009) We may apply these weights in the processof solving a MCDM problem In addition these weightsdisplay that indicator 1 is more significant than others (seeTable 1) In this case the grade arrangement of these indicatorsis as follows

1198821gt 1198822gt 1198823 (16)

The results of ranking these criteria are presented in Table 1

36 FAHP Method The AHP approach applies multicriteriadecision analysis developed 119887 presented by Saaty [28] tocompute the weighting factor of attribute The AHP methodis constructed on the pairwise comparison to compute the

Advances in Materials Science and Engineering 5

Table 1 The result of ranking of proposed method

Criterion Weight Rank1 119882

1= 06334 1

2 1198822= 02678 2

3 1198823= 00987 3

Alternative 2Alternative 1 Alternative 3

Criterion 2 Criterion 3Criterion 1

Goal

Figure 3 A hierarchical structure

weight of each criterion The AHP permits experts to deter-mine the significance of each criterion during comparingother criteria from 1 to 9 from ldquosame importancerdquo (1)to ldquocompletely more importantrdquo (9) Building a decisiontree decision-maker is permitted to first describe weightsof the main criteria and then decision-maker can describethe lower level subcriteria that exactly describe the testedmulticriteria issue [28]

The AHP method may not handle the ambiguity indetermining the rankings of various attributes [29] Alsoit is usually hard to evaluate various factors because of alack of suitable data In FAHP method quid pro quo ofallocating definite quantities the adjudications are built byapplying linguistic parameters and are characterized by fuzzymembership functionsThe fuzzy geometric mean method isthe most accepted method to construct the matrix The relictprocedures are just routine AHP

37 Proposed Algorithm An algorithm to determine themostpreferable aluminum waste management system selectionamong all possible alternatives when data is fuzzy by usingGP and the NWIA with the extended AHP method is givenin the following

Step 1 (set up the expert group) To evaluate alternatives anexpert group comprised of researcher and managers shouldbe formed

Step 2 Create a hierarchical structure of elements for prob-lem solving For this propose it is necessary for decision-makers to determine criteria and subcriteria based onproposing the main target See for example Figure 3

Step 3 Build a set of fuzzy comparison matrices for eachdecision-maker

Step 4 (aggregate fuzzy comparison matrices) We aggregatefuzzy comparison matrices constructed by decision-makers

by using the geometric mean method and convert them tounit fuzzy comparison matrix

where 119886119871119894119895= (

5

prod

119896=1

119886119871119896

119894119895)

15

119886119872

119894119895= (

5

prod

119896=1

119886119872119870

119894119895)

15

119886119880

119894119895= (

5

prod

119896=1

119886119880119870

119894119895)

15

(119886119871119896

119894119895 119886119872119870

119894119895 119886119880119870

119894119895) 119896 = 1 2 5

(17)

is the important opinion of the119870th decision-maker

Step 5 (deriving theweights of eachmatrix) For this purposewe apply the following substeps

Step 51 By using (7) we convert each fuzzy matrix to aninterval fuzzy matrix

Step 52 By resolving model (12) we can achieve the weightof each comparison matrix

Step 6 (aggregate the weights and rank the alternatives) Weaggregate the weights and rank the alternatives and finallyselect the best aluminum waste management system Thepriorityweight of each optionmay be achieved bymultiplyingthe matrix of assessment by the vector of characteristicweights and adding over all characteristics [30]

4 Case Study

A case study on aluminum manufacturers and particularlyaluminum remelter plants in Arak an industrial city in Iranis introduced It illustrates how the proposed fuzzy AHPmethodology according to the algorithm can be applied toselecting the best aluminum waste management system

Twenty-nine remelting facilities were incorporated in thisresearch The secondary aluminum remelting is consideredas a unit function As shown in Figure 4 this process unitincludes the storage in place (1) beneficiation activities (2)related to input aluminum scrap such as washing separatingand sorting (orwithout beneficiation activities (3)) remeltingin the crucible furnace (4) duplicate aluminum black drossrecycling in plant (5) (or exporting aluminum black drossto another place and duplicate recycling (6)) and final wastelandfilling (7) (or release in the environment (8))

All the results are based on the reference flow of 1 tonof aluminum batch including new and old aluminum scrapsand white and black aluminum dross (see Figure 5) Theupkeep and repair of the plant and equipment materialsare provided to this life cycle stage from both primaryand secondary aluminum processing Also the secondaryremelters have a diversity of melting furnaces top-loadedclosed rotary and side well-feeding melting They have

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

Table 1 The result of ranking of proposed method

Criterion Weight Rank1 119882

1= 06334 1

2 1198822= 02678 2

3 1198823= 00987 3

Alternative 2Alternative 1 Alternative 3

Criterion 2 Criterion 3Criterion 1

Goal

Figure 3 A hierarchical structure

weight of each criterion The AHP permits experts to deter-mine the significance of each criterion during comparingother criteria from 1 to 9 from ldquosame importancerdquo (1)to ldquocompletely more importantrdquo (9) Building a decisiontree decision-maker is permitted to first describe weightsof the main criteria and then decision-maker can describethe lower level subcriteria that exactly describe the testedmulticriteria issue [28]

The AHP method may not handle the ambiguity indetermining the rankings of various attributes [29] Alsoit is usually hard to evaluate various factors because of alack of suitable data In FAHP method quid pro quo ofallocating definite quantities the adjudications are built byapplying linguistic parameters and are characterized by fuzzymembership functionsThe fuzzy geometric mean method isthe most accepted method to construct the matrix The relictprocedures are just routine AHP

37 Proposed Algorithm An algorithm to determine themostpreferable aluminum waste management system selectionamong all possible alternatives when data is fuzzy by usingGP and the NWIA with the extended AHP method is givenin the following

Step 1 (set up the expert group) To evaluate alternatives anexpert group comprised of researcher and managers shouldbe formed

Step 2 Create a hierarchical structure of elements for prob-lem solving For this propose it is necessary for decision-makers to determine criteria and subcriteria based onproposing the main target See for example Figure 3

Step 3 Build a set of fuzzy comparison matrices for eachdecision-maker

Step 4 (aggregate fuzzy comparison matrices) We aggregatefuzzy comparison matrices constructed by decision-makers

by using the geometric mean method and convert them tounit fuzzy comparison matrix

where 119886119871119894119895= (

5

prod

119896=1

119886119871119896

119894119895)

15

119886119872

119894119895= (

5

prod

119896=1

119886119872119870

119894119895)

15

119886119880

119894119895= (

5

prod

119896=1

119886119880119870

119894119895)

15

(119886119871119896

119894119895 119886119872119870

119894119895 119886119880119870

119894119895) 119896 = 1 2 5

(17)

is the important opinion of the119870th decision-maker

Step 5 (deriving theweights of eachmatrix) For this purposewe apply the following substeps

Step 51 By using (7) we convert each fuzzy matrix to aninterval fuzzy matrix

Step 52 By resolving model (12) we can achieve the weightof each comparison matrix

Step 6 (aggregate the weights and rank the alternatives) Weaggregate the weights and rank the alternatives and finallyselect the best aluminum waste management system Thepriorityweight of each optionmay be achieved bymultiplyingthe matrix of assessment by the vector of characteristicweights and adding over all characteristics [30]

4 Case Study

A case study on aluminum manufacturers and particularlyaluminum remelter plants in Arak an industrial city in Iranis introduced It illustrates how the proposed fuzzy AHPmethodology according to the algorithm can be applied toselecting the best aluminum waste management system

Twenty-nine remelting facilities were incorporated in thisresearch The secondary aluminum remelting is consideredas a unit function As shown in Figure 4 this process unitincludes the storage in place (1) beneficiation activities (2)related to input aluminum scrap such as washing separatingand sorting (orwithout beneficiation activities (3)) remeltingin the crucible furnace (4) duplicate aluminum black drossrecycling in plant (5) (or exporting aluminum black drossto another place and duplicate recycling (6)) and final wastelandfilling (7) (or release in the environment (8))

All the results are based on the reference flow of 1 tonof aluminum batch including new and old aluminum scrapsand white and black aluminum dross (see Figure 5) Theupkeep and repair of the plant and equipment materialsare provided to this life cycle stage from both primaryand secondary aluminum processing Also the secondaryremelters have a diversity of melting furnaces top-loadedclosed rotary and side well-feeding melting They have

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

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CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

(4)

Skimming

Aluminum industries

(5)

Aluminum ingot

(3)

(8) (6)

Aluminum dross storage(7)

(Emission to water)

(Emission to soil)

(Emission to air)

(1) (2)

Figure 4 Flowchart of the secondary aluminum remelting in proposed research

different competence In this study the crucible furnace forthe secondary aluminum remelting is used

In this study firstly a panel of experts as the decision-maker group was set up The decision-makers were fiveexperts three engineers from the production managers ofaluminum industries and two academics in the environmentand management fields Then literature financial docu-ments statistics of occupational accidents the results ofoverviews and the primary LCA were evaluated by thedecision-makers using fuzzy linguistic terms This approachallowed us to mathematically represent uncertainty andvagueness and reflect the decision-makerrsquos perception ofdecision-making process After this a questionnaire was dis-tributed to the decision-makers to evaluate and characterizethe importance weights of the criteria and ratings of theoptions

Once the answers were collected the questionnaireresults were studied and the discussions were directed toconfirm the data reliability Figure 6 shows the decisionhierarchy for the decision-making issue In the upper ranks ofthe hierarchy we have the general aim which in this instanceis the choice of an aluminum waste management system Wepresented the main criteria including environmental socialand economic aspects at level 2 The associated commonattributes or subcriteria (level 3) are the main criteria Thesegeneral attributes are broken down into global warming(GWP) human toxicity (HTP) land use (LU) health andsafety at work (HampS) regulation (Reg) turnover and gainAt level 4 we showed five management options

Five management alternatives for aluminum waste man-agement in Arak are presented as follows

(i) Alternative ldquoArdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg benefici-ation activities related to input aluminum scrap

such as washing separating and sorting exportingaluminum black dross to another place duplicaterecycling and landfill

(ii) Alternative ldquoBrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminumwith a grade 96 (scrap) including 800 kgremelting without beneficiation activities exportingremaining aluminumblack dross to another place andduplicate recycling and release in the environment

(iii) Alternative ldquoCrdquo aluminum crucible for remeltingaluminum batch includes the primary aluminumingot 995 including 200 kg and the secondaryaluminum 96 (scrap) including 800 kg beneficia-tion activities related to input aluminum black scrapsuch as washing separating and sorting duplicatealuminum dross recycling in plant and landfill

(iv) Alternative D defined as the present current alu-minum waste management system aluminum cru-cible for remelting aluminum batch includes the pri-mary aluminum ingot 995 including 200 kg and thesecondary aluminum 96 (scrap) including 800 kgremelting without beneficiation activities exportingaluminum black dross to another place and duplicaterecycling and release in the environment

(v) Alternative E aluminum crucible for remelting alu-minum batch includes the primary aluminum ingot995 including 200 kg and the secondary aluminum98 (scrap) including 800 kg beneficiation activitiesrelated to input aluminum scrap such as washingseparating and sorting duplicate aluminum blackdross recycling in plant and landfill

Alternative ldquoArdquo is defined as the ldquointermediaterdquo waste man-agement system Alternative B is defined as the current

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

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CompositesJournal of

NanoparticlesJournal of

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Biomaterials

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Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

(a) New aluminum scrap (b) Old aluminum scrap

(c) White aluminum dross (d) Black aluminum dross

Figure 5 Aluminum wastes in the proposed study

Aluminum waste management system selection

Alternative A Alternative B Alternative C Alternative D Alternative E

Criterion C3 Criterion C1 Criterion C2

Turnover C31 Gain C21 GWP C11 LU C12 EPT C13 HampS C21 Reg C22

Figure 6 The hierarchical structure in the proposed research

waste management system It is similar to alternative A butinstead of landfill method the aluminum waste is released inthe environment Alternative C represents ldquobusinessrdquo optionwhere economic benefits are more important AlternativeD represents ldquowaste exportrdquo where approximately 70 ofaluminum waste that is normally landfilled is exported toanother place to duplicate recycling Alternative E is definedas the environmentally friendly system

Pairwise comparison concerning the main target is pre-sented in Table 2

Pairwise comparison matrix subcriteria concerning thebasic criteria are presented in Table 3

Comparison matrix subcriteria concerning the alterna-tives are as in Tables 4ndash10

Table 2 Criteria concerning the main target

Main target C1

C1

C1

C1

(1 1 1) (422 626 828) (472 626 828)C2

(012 016 021) (1 1 1) (3 5 7)C3

(012 016 021) (014 02 033) (1 1 1)

The results of interval approximation of pairwise compar-ison matrices are presented in Tables 11ndash19

The calculating of weighted approximation related toTable 12 is presented in Example 2

As shown in Table 20 alternative ldquoErdquo is assigned as themost preferable choice with a weight of 0594161 alternative

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

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CompositesJournal of

NanoparticlesJournal of

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International Journal of

Biomaterials

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and Engineering

Table 3 Subcriteria concerning the main criteria

(a)

Environmental (C1) C

11C12

C13

C11 (1 1 1) (118 276 356) (084 118 191)

C12 (019 036 058) (1 1 1) (208 292 528)

C13 (052 084 118) (018 034 048) (1 1 1)

(b)

Social (C2) C

21C22

C21

(1 1 1) (208 292 366)C22

(027 034 048) (1 1 1)

(c)

Economical (C3) C

31C32

C31

(1 1 1) (208 421 626)C32

(016 024 048) (1 1 1)

Table 4 Purposed options concerning GWP subcriteria

(GWP) C11

A B C D EA (1 1 1) (144 355 56) (034 046 058) (1 3 5) (015 016 019)B (026 030 041) (1 1 1) (011 014 014) (02 033 1) (011 014 014)C (1 229 5) (7 7 9) (1 1 1) (3 5 7) (016 024 048)D (02 033 1) (1 3 5) (014 02 025) (1 1 1) (011 014 016)E (422 625 827) (7 7 9) (208 421 626) (56 7 9) (1 1 1)

Table 5 Options concerning the ETP subcriteria

(ETP) C12

A B C D EA (1 1 1) (1 3 5) (021 025 03) (1 1 3) (013 019 030)B (014 024 028) (1 1 1) (011 014 014) (023 048 1) (011 014 014)C (208 421 626) (7 7 9) (1 1 1) (5 7 9) (021 023 036)D (033 1 1) (1 208 422) (012 016 024) (1 1 1) (011 014 016)E (191 397 608) (625 7 9) (208 421 626) (625 7 9) (1 1 1)

Table 6 Options concerning LU subcriteria

(LU) C13

A B C D EA (1 1 1) (422 625 826) (033 1 1) (144 355 56) (018 028 069)B (013 018 028) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 5 7) (023 048 1)D (018 028 069) (1 1 3) (014 02 033) (1 1 1) (011 014 014)E (144 355 559) (7 7 9) (1 208 421) (7 7 9) (1 1 1)

Table 7 Options concerning HampS subcriteria

HampS (C21) A B C D E

A (1 1 1) (024 028 052) (024 028 052) (011 014 014) (011 014 018)B (208 421 626) (1 1 1) (033 1 1) (014 02 033) (024 048 1)C (208 421 626) (1 1 3) (1 1 1) (024 033 058) (033 1 1)D (7 7 9) (3 5 7) (1 3 5) (1 1 1) (1144 355)E (625 7 9) (1 208 42) (1 3 5) (04 07 07) (1 1 1)

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Nano

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Journal ofNanomaterials

Advances in Materials Science and Engineering 9

Table 8 Options concerning regulation subcriteria

(Reg) C22

A B C D EA (1 1 1) (3 57) (033 1 1) (1 3 5) (02 033 1)B (014 02 033) (1 1 1) (011 014 014) (1 1 1) (011 014 014)C (07 1 2) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (1 1 1) (014 02 033) (1 1 1) (011 014 014)E (1 3 5) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 9 Options concerning turnover subcriteria

(Turnover) C31

A B C D EA (1 1 1) (355 559 761) (033 1 1) (1 3 5) (013 024 028)B (014 02 033) (1 1 1) (011 014 014) (033 1 1) (011 014 014)C (1 1 3) (7 7 9) (1 1 1) (3 57) (1 1 1)D (02 033 1) (069 1 1) (012 016 024) (1 1 1) (011 014 014)E (355 418 761) (7 7 9) (1 1 1) (7 7 9) (1 1 1)

Table 10 Options concerning gain subcriteria

(Gain) C32

A B C D EA (1 1 1) (058 14 292) (028 069 1) (121 202 366) (208 421 625)B (034 069 17) (1 1 1) (109 17 25) (1 208 421) (625 7 9)C (1 1 3) (039 058 092) (1 1 1) (018 028 069) (1 1 1)D (027 049 082) (02 033 1) (1 3 5) (1 1 1) (5 7 9)E (013 024 028) (011 014 02) (1 1 1) (013 014 019) (1 1 1)

Table 11 The interval approximation main target concerning thegain criteria

Main target C1

C2

C3

Obtained weightsC1

[1 1] [57 68] [57 68] 084507C2

[015 018] [1 1] [45 55] 0126761C3

[015 018] [018 023] [1 1] 0028169

Table 12 The interval approximation subcriteria concerning themain criteria

(a)

Environment C11

C12

C13

Obtainedweights

C11 [1 1] [236

296] [109 137] 0633438

C12 [032 042] [1 1] [271 351] 0267838

C13 [076 093] [030

038] [1 1] 0098724

(b)

Social C21

C22

Obtained weightsC21

[1 1] [27 31] 0754717C22

[032 047] [1 1] 0245283

(c)

Economic C31

C32

Obtained weightsC31

[1 1] [368 473] 0821693C32

[022 03] [1 1] 0178307

ldquoCrdquo with a value of 0198146 alternative ldquoArdquo with a valueof 0090549 alternative ldquoDrdquo with a value of 0070878 andalternative ldquoBrdquo with a value of 0036346 are in next orderrespectively

5 Comparison with Other Existing Methods

In addition the fuzzy AHP methods in the literature arecompared [30 31] as shown in Table 21 There are significantdifferences in their hypothetical forms The comparisonincludes positives and negative points of each method Mainpositives of proposed method were assigned at the bottomof Table 21 and were denoted with bold font For evaluationof proposed method we applied Changrsquos method [32] inorder to assess the aluminumwastemanagement systems (seeTable 22)

6 Discussion

As was previously noted the secondary aluminum pro-duction increases quickly due to environmental issues andcontinuous growing of use demands In this case over 200kilograms of aluminum black dross as waste is producedfor each ton of secondary aluminum black dross is eitherduplicate recovered as by-products or landfilled Howeverreleasing this quantity in environment can produce consid-erable consequences from the air the water and the soilpollution point of view Recovery recycle and disposal ofaluminum wastes including aluminum dross and aluminumscrap are a global issue in terms of environmental social

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

Table 13 The interval approximation purposed choices referring to GWP subcriteria

GWP A B C D E Obtained weightsA [1 1] [302 406] [033 04] [25 35] [015 017] 0090862B [028 031] [1 1] [013 014] [03 05] [014 014] 0026054C [196 296] [7 75] [1 1] [45 55] [023 027] 0195402D [03 05] [25 35] [018 021] [1 1] [013 014] 0036345E [57 676] [7 75] [368 472] [68 75] [1 1] 0651339

Table 14 The interval approximation choices referring to ETP subcriteria

ETP A B C D E Obtained weightsA [1 1] [25 35] [022 021] [1 15] [018 022] 0041578B [042 061] [1 1] [013 015] [042 061] [014 014] 0024023C [368 472] [7 75] [1 1] [65 75] [023 027] 0180174D [083 1] [18 26] [015 018] [1 1] [013 014] 0027719E [35 45] [68 75] [368 472] [68 75] [1 1] 0726506

Table 15 The interval approximation choices referring to LU subcriteria

LU A B C D E Obtained weightsA [1 1] [574 667] [083 1] [302 406] [025 038] 0173079B [017 02] [1 1] [013 015] [1 087] [013 015] 0030116C [1 15] [7 75] [1 1] [45 55] [05 06] 0223084D [025 038] [1 15] [018 023] [1 1] [013 015] 0042567E [3 4] [7 75] [18 26] [7 75] [1 1] 0531153

Table 16 The interval approximation choices referring to HampS subcriteria

HampS A B C D E Obtained weightsA [1 1] [021 025] [027 034] [013 014] [013 015] 0037196B [368 472] [1 1] [083 1] [018 023] [042 061] 0109401C [368 472] [1 15] [1 1] [013 014] [083 1] 0164101D [7 75] [45 55] [25 35] [1 1] [13 197] 0492303E [68 75] [18 26] [1 15] [062 069] [1 1] 0197

Table 17 The interval approximation choices referring to the regulation subcriteria

Regulation A B C D E Obtained weightsA [1 1] [45 55] [083 1] [25 35] [03 05] 0247475B [018 023] [1 1] [013 014] [1 1] [013 014] 0045455C [092 13] [7 75] [1 1] [45 55] [1 1] 0318182D [03 025] [1 1] [018 023] [1 1] [013 014] 0070707E [25 35] [7 75] [1 1] [7 75] [1 1] 0318182

Table 18 The interval approximation choices referring to turnover subcriteria

Turnover A B C D E Obtained weightsA [1 1] [508 609] [083 1] [25 35] [015 017] 0224165B [032 042] [1 1] [013 014] [092 1] [013 014] 0044833C [1 15] [681 75] [1 1] [574 676] [1 1] 0336247D [030 038] [092 1] [015 017] [1 1] [013 014] 0058508E [443 544] [7 75] [1 1] [7 75] [1 1] 0336247

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

Table 19 The interval approximation options concerning gain subcriteria

Gain A B C D E Obtained weightsA [1 1] [122 181] [059 077] [182 243] [368 472] 0322223B [060 095] [1 1] [0028 0169] [181 261] [681 75] 0305145C [018 023] [054 067] [1 1] [025 038] [1 1] 0159262D [1 15] [03 05] [030 038] [1 1] [65 75] 0168588E [021 028] [013 015] [236 296] [014 016] [1 1] 0044782

Table 20 The results of ranking aluminum waste managementsystem options

Alternatives Final obtained weights Rank of alternativesA 0090549 3B 0036346 5C 0198146 2D 0070878 4E 0594161 1Ranking order E gt C gt A gt D gt B

and economic aspects The presented model for industrialwaste management alternatives was implemented in the caseof aluminum waste systems in the industrial city of ArakThe application of LCA to the aluminum waste managementsystem will be a feasible way However LCA works havecommonly an intrinsic ambiguity due to different categoriesIn addition no single solution is available as each industryin each country has different characteristics in terms ofgeographical and environmental as well as social and eco-nomic aspects Several management decisions are requiredto provide efficient aluminum waste management systemsThe objective of this research is to propose an integratedFAHP in the aluminum waste management system Themodel for the aluminum waste management system whichintegrates social economic and environmental aspects isthe MCDM problem This study has presented a modelbased on the fuzzy concept to compare aluminum wastemanagement systems It may mainly evaluate and containsinterdependence relationship amongst the criteria underambiguity The results of the research represent that themethod is easy in computation and setting priorities Henceit is mainly appropriate for solving MCDM problems Atthis research we apply environmental social and economiccriteria for evaluation and support decision-making withinthe aluminum industry as theMCDMproblem On the otherhand the fuzzy AHP can be utilized not only as a methodto handle the interdependence within a collection of criteriabut also as a method of generating more noteworthy datafor decision-making The model also has disadvantages Forexample FAHP model uses the aggregated categoriesrsquo datathat several subcategories are evaluated under the same maincategory This will increase the uncertainty in FAHP basedon LCA results that can be solved by using more specificlife cycle data for several steps of aluminum waste It issignificant to regard that the weights of subcriteria obtainedfrom expert judgment are also subject to uncertainties With

changing weights a fuzzy MCDM decision-making methodmight give different results for the ranking of aluminumwastemanagement alternatives Seven subcriteria are consideredfrom a group of three main criteria namely environmentalsocial and economic First decision-makers evaluated eachwaste management alternative for selected criteria and sub-criteria Second we obtained these evaluation results takinginto account the weight of the criteria and subcriteria Alsowe transformed collected data into the fuzzy intuitionisticversion Finally we applied a real MCDM problem for theproposed decision-making method The model aims to rankwaste management alternatives Relevant to the outcomes ofexpert judgment the most important environmental subcri-teria are determined as global warming human toxicity andland use The most influential social indicator is indicatedas health and safety at work and regulation and the mostinfluential economic subcriteria are determined as turnoverand gain

The results showed that alternative E has the highestranking compared to other alternatives Also alternative Cand alternative A are ranked third and fourth respectivelyApart from these three other alternatives of aluminumwaste management system as alternative D and alternativeB ranked fourth and fifth respectively Each alternativepresents a solution for the aluminum waste managementsystem with a certain degree of trade-off between benefitand its consequences related to environmental social andeconomic issues For example the choice of alternative Ccould be increased by the increasing amount of aluminumscraps related to the primary aluminum production processAlso alternative D represents the export of aluminum wasteto other places in the form of black dross or aluminumdross with less metallurgic aluminum From the applicationperspective this research will provide a valuable insight formanagers to attempt to improve the environmental socialand economic condition all together at the same time

7 Conclusions

Nowadays thanks to increased awareness and importantenvironmental pressures from various stakeholders environ-mental issues in daily activities are considered by industriesHowever so far little attention has been given to environ-mental aspects of processing output of aluminum dross andaluminum scrap as aluminum waste All the informationcollected was related to LCA result written documents andfindings from interviews For the proposed integrated fuzzyAHP model the five alternatives are investigated In thisstudy we applied the NWIA of FN to transform each fuzzy

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 Advances in Materials Science and Engineering

Table 21 The comparison of various FAHP models [30 31]

Sources Basic specifications Positives (P)negatives (N)

[15]

Direct extension of Saatyrsquos AHP model with triangularfuzzy numbers

(P) The judgments of multiple experts may be modeledin the reciprocal matrix

Lootsmarsquos logarithmic least square model is used toderive fuzzy weights and fuzzy performance scores

(N) Evermore there is no solution to the linearequations(N)The calculational demand is great even for a lowproblem(N) It permits only triangular FN to be applied

[16]

Direct extension of Saatyrsquos AHP model with trapezoidalfuzzy numbers (P) It is simple to extend to the fuzzy term

Uses the geometric mean model to derive fuzzy weightsand performance scores

(P) It guarantees an alone solution to the reciprocalcomparison matrix(N)The calculational demand is great

[33]Modifies van Laarhoven and Pedryczrsquos model (P) The judgments of multiple experts may be modeledShows a more robust method to the normalization ofthe local priorities (N)The calculational demand is great

[32]

Synthetical degree values (P) The calculational demand is partly low

Layer simple sequencing (P) It follows the steps of crisp AHP it does not involveadditional process

Composite total sequencing (N) It permits only triangular FN to be applied

[32]

Creates fuzzy standards (P) The calculational demand is not great

Illustrates performance numerals by membershipfunctions

(N) Entropy is applied when probability distribution isknown The model is based on both probability andpossibility measures

Uses entropy concepts to calculate aggregate weights

Proposed method Uses interval approximation to defuzzification (P) It permits all FN to be applied(P) It retains uncertainty of fuzzy number in itself

Uses goal programming method to obtain weights (P) It is done mainly with a software such as Lingo

Table 22 The comparison of results of proposed method and Changrsquos fuzzy AHP method

Alternatives Weights (proposed) Rank of alternatives Weights (Changrsquos method) Rank of alternativesA 0090549 3 0094855 3B 0036346 5 0006343 5C 0198146 2 0305851 2D 0070878 4 001511 4E 05941 1 0409039 1Ranking order (the proposed method) E gt C gt A gt D gt BRanking order (Changrsquos method) E gt C gt A gt D gt B

component of the pairwise matrix to its NWIA Then weapplied the GPmodel for weighting and LINGO 11 to resolveThe results showed that alternative E and alternative B areassigned as the best and the worst preferred choice withweights of 0594161 and 0036346 respectively In alternativeE aluminum batch includes primary aluminum ingot 995ndash20 and secondary aluminum (aluminum scrap 98ndash80)beneficiation activities related to input aluminum scrap suchas washing separating and sorting duplicate aluminumdross recycling in plant and landfill while in alternative Baluminumbatch includes primary aluminum ingot 995ndash20and secondary aluminum (aluminum scrap 96ndash80) remelt-ing without beneficiation activities exporting remaining

aluminum dross to other places and duplicate recycling andrelease in the environment

According to above-mentioned consideration uncer-tainty in the LCA results and limitations of the currentmethod should be taken into account by decision-makersFirst of all the methodology may be utilized for similarproblems where multiple criteria are present This researchwill supply a valuable insight for the directors to try toimprove the environmental social and economic condi-tion all together simultaneously In future research currentfuzzy approach can be developed and applied for differentMCDM problems in industry where conflicting criteriaexist

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J-P Hong J Wang H-Y Chen B-D Sun J-J Li and C ChenldquoProcess of aluminum dross recycling and life cycle assessmentfor Al-Si alloys and brown fused aluminardquo Transactions ofNonferrousMetals Society of China vol 20 no 11 pp 2155ndash21612010

[2] S Khamis M Lajis and R Albert ldquoA sustainable directrecycling of aluminum chip (AA6061) in hot press forgingemploying response surface methodologyrdquo Procedia CIRP vol26 pp 477ndash481 2015

[3] T Norgate and S Jahanshahi ldquoReducing the greenhouse gasfootprint of primary metal production where should the focusberdquoMinerals Engineering vol 24 no 14 pp 1563ndash1570 2011

[4] G Liu C E Bangs and D B Muller ldquoStock dynamics andemission pathways of the global aluminium cyclerdquo NatureClimate Change vol 3 no 4 pp 338ndash342 2013

[5] G Liu and D B Muller ldquoAddressing sustainability in thealuminum industry a critical review of life cycle assessmentsrdquoJournal of Cleaner Production vol 35 pp 108ndash117 2012

[6] M C Shinzato and R Hypolito ldquoSolid waste from aluminumrecycling process characterization and reuse of its economicallyvaluable constituentsrdquoWasteManagement vol 25 no 1 pp 37ndash46 2005

[7] H I Gomes W M Mayes M Rogerson D I Stewart and IT Burke ldquoAlkaline residues and the environment a review ofimpacts management practices and opportunitiesrdquo Journal ofCleaner Production 2015

[8] P H Brunner and H Rechberger ldquoWaste to energymdashkey ele-ment for sustainable waste managementrdquo Waste Managementvol 37 pp 3ndash12 2015

[9] A Abdulkadir A Ajayi and M I Hassan ldquoEvaluating thechemical composition and the molar heat capacities of a whitealuminum drossrdquo Energy Procedia vol 75 pp 2099ndash2105 2015

[10] S O AdeosunM A UsmanW A Ayoola and I O SekunowoldquoEvaluation of the mechanical properties of polypropylene-aluminum-dross compositerdquo ISRN Polymer Science vol 2012Article ID 282515 6 pages 2012

[11] T W Unger and M Beckmann ldquoSalt slag processing forrecyclingrdquo in Proceedings of the Sessions Light Metals TMSAnnualMeeting (TMS rsquo92) pp 1159ndash1162 SanDiego Calif USA1992

[12] A Weckenmann and A Schwan ldquoEnvironmental Life CycleAssessment with support of fuzzy-setsrdquoThe International Jour-nal of Life Cycle Assessment vol 6 no 1 pp 13ndash18 2001

[13] L P Guereca N Agell S Gasso and J M Baldasano ldquoFuzzyapproach to life cycle impact assessmentrdquo The InternationalJournal of Life Cycle Assessment vol 12 no 7 pp 488ndash496 2007

[14] J Seppala ldquoOn the meaning of fuzzy approach and normalisa-tion in life cycle impact assessmentrdquo The International Journalof Life Cycle Assessment vol 12 no 7 pp 464ndash469 2007

[15] P J M Van Laarhoven and W Pedrycz ldquoA fuzzy extension ofSaatyrsquos priority theoryrdquo Fuzzy Sets and Systems vol 11 no 1ndash3pp 229ndash241 1983

[16] R C Buckley ldquoDistinguishing the effects of area and habitattype on island plant species richness by separating floristic ele-ments and substrate types and controlling for island isolationrdquoJournal of Biogeography vol 12 no 6 pp 527ndash535 1985

[17] M Weck F Klocke H Schell and E Ruenauver ldquoEvaluatingalternative production cycles using the extended fuzzy AHPmethodrdquo European Journal of Operational Research vol 100 no2 pp 351ndash366 1997

[18] M R Abdi ldquoFuzzy multi-criteria decision model for evaluatingreconfigurable machinesrdquo International Journal of ProductionEconomics vol 117 no 1 pp 1ndash15 2009

[19] H K Chan X Wang G R T White and N Yip ldquoAn extendedfuzzy-AHP approach for the evaluation of green productdesignsrdquo IEEE Transactions on Engineering Management vol60 no 2 pp 327ndash339 2013

[20] L Wang H Zhang and Y-R Zeng ldquoFuzzy analytic hierarchyprocess (FAHP) and balanced scorecard approach for evaluat-ing performance of Third-Party Logistics (TPL) enterprises inChinese contextrdquo African Journal of Business Management vol6 no 2 pp 521ndash529 2012

[21] G Zheng Y Jing H Huang and Y Gao ldquoApplying LCA andfuzzy AHP to evaluate building energy conservationrdquo CivilEngineering and Environmental Systems vol 28 no 2 pp 123ndash141 2011

[22] C-Y Lin A H I Lee and H-Y Kang ldquoAn integrated newproduct development frameworkmdashan application on green andlow-carbon productsrdquo International Journal of Systems Sciencevol 46 no 4 pp 733ndash753 2015

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[24] S-J C C-L Hwang and F P Hwang Fuzzy Multiple AttributeDecision Making Springer 1992

[25] J Ramık and P Korviny ldquoInconsistency of pair-wise compar-ison matrix with fuzzy elements based on geometric meanrdquoFuzzy Sets and Systems vol 161 no 11 pp 1604ndash1613 2010

[26] M Izadikhah ldquoDeriving weights of criteria from inconsistentfuzzy comparison matrices by using the nearest weightedinterval approximationrdquo Advances in Operations Research vol2012 Article ID 574710 17 pages 2012

[27] G-H Tzeng and J-J Huang Fuzzy Multiple Objective DecisionMaking CRC Press 2013

[28] T L Saaty ldquoWhat is the analytic hierarchy processrdquo inMathe-matical Models for Decision Support vol 48 ofNATOASI Seriespp 109ndash121 Springer Berlin Germany 1988

[29] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[30] Z Ayag and R G Ozdemir ldquoA fuzzy AHP approach toevaluating machine tool alternativesrdquo Journal of IntelligentManufacturing vol 17 no 2 pp 179ndash190 2006

[31] G Buyukozkan C Kahraman and D Ruan ldquoA fuzzy multi-criteria decision approach for software development strategyselectionrdquo International Journal of General Systems vol 33 no2-3 pp 259ndash280 2004

[32] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

[33] C G Boender J G De Graan and F A Lootsma ldquoMulti-criteria decision analysis with fuzzy pairwise comparisonsrdquoFuzzy Sets and Systems vol 29 no 2 pp 133ndash143 1989

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials