SupplierSelectionofShipbuildingEnterprisesBasedon ...sets. Intuitionistic fuzzy sets use two scales...

Research ArticleSupplier Selection of Shipbuilding Enterprises Based onIntuitionistic Fuzzy Multicriteria Decision

Xiang Ziquan Yang Jiaqi Muhammad Hamza Naseem Xiang Zuquan and Liang Xueheng

School of Transportation Wuhan University of Technology Wuhan 430063 China

Correspondence should be addressed to Xiang Ziquan xiangziquanwhuteducn

Received 30 April 2021 Revised 26 June 2021 Accepted 13 July 2021 Published 22 July 2021

Academic Editor Edyta Kucharska

Copyright copy 2021 Xiang Ziquan et al +is 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

With the increasingly fierce competition in the global shipbuilding industry shipbuilding enterprises need to maintain com-petitiveness and cope with rapid changes In this case shipbuilding enterprises need to establish effective supply chain man-agement Among them choosing the right supplier is one of the most critical activities +e supplier selection of shipbuildingenterprises is considered a complex multicriteria decision-making (MCDM) problem that attracts much attention due tointuitionistic fuzzy sets to deal with possible imprecision and fuzziness in real life Based on this this paper proposes a newmethodbased on the intuitionistic fuzzy SWARA (stepwise weight assessment ratio analysis) and COPRAS (complex proportionalassessment) method to select shipbuilding enterprise suppliers which is a new research area First of all different weights are givento each expert evaluation result according to their position educational background and working years +e supplier indexrsquosweight is determined based on the intuitionistic fuzzy SWARA method and it is easy to understand and operate +e ranking ofsuppliers is determined by the intuitionistic fuzzy COPRAS method +is method considers all kinds of uncertainties andevaluates the utility index and the cost index of alternative suppliers Finally taking a shipbuilding enterprise as an exampleapplying the intuitionistic fuzzy SWARA-COPRAS method is illustrated Compared with other methods and sensitivity analysisit shows that the intuitionistic fuzzy multicriteria decision-making method is effective and stable in shipbuilding enterprises

1 Introduction

In todayrsquos fiercely competitive environment shipbuildingcompanies are facing many challenges Supplier selection isone of the most important activities for shipbuildingcompanies +e issue of supplier selection for shipbuildingcompanies is a critical area in the shipbuilding supply chain+e allocation of orders to multiple suppliers by enterprisesis a complex multiobjective decision-making problem re-stricted by many factors such as purchase price purchasequality product delay quantity product complaint quantityand supplier supply capacity +erefore shipbuilding en-terprises should comprehensively consider the various de-cisions that affect the order allocation so as to maximize thebenefits

+e supplier selection problem of shipbuilding enter-prises is an uncertain fuzzy multicriteria decision-making

(MCDM) problem In practice due to the complexity ofshipbuilding enterprise problems the limitations of deci-sion-makersrsquo knowledge the fuzziness of information ofalternative suppliers and the high cost of obtaining theaccurate information of shipbuilding enterprises manycriteria decision-making problems are often accompaniedby many uncertainties To solve this problem fuzzy set andfuzzy logic are introduced to model and describe uncertaininformation by fuzzy number A fuzzy set theory exists inmany practical economic management decision-makingproblems +e fuzzy set theory proposed by Professor Zadehin 1965 provides an effective method for dealing withambiguity Professor Zadeh used a single scale (ie degree ofmembership) to define fuzzy sets that is a single degree ofmembership simultaneously expresses the two opposites offuzziness fuzzy concepts or fuzzy phenomena +is idea isbased on the dichotomy it cannot express the neutral state

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 1775053 11 pageshttpsdoiorg10115520211775053

(neither support nor opposition) In 1986 Bulgarian scholarKT Atanassov proposed the concept of intuitionistic fuzzysets Intuitionistic fuzzy sets use two scales (degree ofmembership and nonsubordination) to characterize ambi-guity simultaneously expressing support opposition andneutrality and can describe the natural attributes of ob-jective phenomena in a more detailed and comprehensivemanner In view of the fluctuation of the market economyand the uncertainty of shipownerrsquos demand this paperproposes a new intuitionistic fuzzy multicriteria decision-making method based on the SWARA (stepwise weightassessment ratio analysis) and COPRAS (complex propor-tional assessment) method In this paper the intuitionisticfuzzy SWARA-COPRAS method is used for the followingreasons (1) Intuitionistic fuzzy sets are a good solution Itcan express decision-makers preferences from three aspectsmembership degree nonmembership degree and hesitationdegree and can more describe the vagueness and uncertaintyof the problem (2) +e method is simple easy to under-stand and easy to implement (3) Transaction costs are lowand decision-makers have more opportunities to set stan-dard priorities

+e contributions of this paper are as follows

(i) Taking into account the vacillation of shipbuildingmarket economy and the uncertainty and diversityof shipownersrsquo demand the corresponding rela-tionship between the linguistic value of expertevaluation and intuitionistic fuzzy set is established

(ii) In the supplier index selection of shipbuilding en-terprises the risk index is included In the selectionof suppliers most of them focus on the cost qualityand service level and rarely take the risk intoaccount

(iii) +e intuitionistic fuzzy SWARA-COPRAS methodis established and applied to a new field supplierselection of shipbuilding enterprises

+e structure of this article is as follows Section 2provides a literature review Section 3 details the intui-tionistic fuzzy multicriteria decision-making method Sec-tion 4 introduces the framework of the intuitionistic fuzzymulticriteria method In Section 5 a shipbuilding companybased in Shanghai China is taken as an example and thealgorithms comparative analysis and the sensitivity analysisshow that the method is effective and stable Section 6 givesthe conclusions of this article

2 Literature Review

21 Supplier Management in Shipbuilding Enterprises In theera of information digitization the essence of the need forcommunication between enterprises and timely exchange ofdemand information drives a new mode of cooperationnamely supply chain management (SCM) With the rapiddevelopment of global economic integration and the in-creasing external competition environment of shipbuildingenterprises the global market competition is becomingmoreandmore intense and SCMhas become an important means

for shipbuilding enterprises to improve their core compe-tition Compared with other manufacturing industriesshipbuilding enterprise supply chain management has itsown uniqueness Shipbuilding has the characteristics ofcustom production +e main impetus of creation comesfrom the end-client transport proprietor which is thegenuine interest chain of ship pulling +ere are many co-operative enterprises in the whole supply chain nodethrough mutual cooperation the whole shipbuilding supplychain management process can be completed

+e supply chain management process of shipbuildingventures with center shipbuilding endeavors as the principlebody is firmly identified with the necessities of shipownersand furthermore includes different materials and hardwareand their providers Shipbuilding is a typical large-scalemanufacturing and assembly industry of on-demand pro-duction +e materials and resources required range fromsupporting equipment plates and profiles to coatings ce-ment and cabin furniture Its suppliers are all over theworld and the number can reach thousands and the ma-terials or equipment provided by these suppliers for ship-building enterprises directly affect the structural design andproduction schedule of ship products As a result changes inessential design technology and schedule information inthe shipbuilding process must be communicated to keysuppliers in a timely manner giving them enough time toalter supply times and inventory levels avoiding resourceloss due to cost increases In addition shipowners will alsopropose to the core shipbuilding enterprises to supply to thedesignated suppliers which requires the core shipbuildingenterprises to establish a good communication environmentbetween shipowners and suppliers to ensure the mutualbenefit of the three parties

22 Shipbuilding Enterprise Supplier Selection MethodRelated research shows that an important part of estab-lishing win-win SCM is to choose agile competitive andcompatible partners namely suppliers +e problem ofsupplier selection for shipbuilding enterprises is one of themain problems of shipbuilding supply chain managementAt present the methods for supplier selection can be roughlydivided into four categories [1] (1) Multiattribute decision-making methods include analytic hierarchy process prior-itize the organization of ranking improvement evaluationmethod network analysis method and approximate idealsolution sorting method (TOPSIS) (2) Mathematical pro-gramming model includes stochastic planning goal plan-ning nonlinear programming data envelopment analysis(DEA) linear programming and multiobjective planning(3) Artificial intelligence technology includes genetic algo-rithm grey system theory neural network rough set theorycase-based reasoning (CBR) particle swarm algorithm antcolony algorithm and fuzzy set theory (FTS) (4) Combi-nation (mixed) model includes AHP+GP AHP+LPAHP+FTS and DEA+MOP Avelina et al [2] studied theparticle swarm optimization (PSO) algorithm and differ-ential evolution (DE) algorithm for supplier selection andorder quantity allocation decision-making problems

2 Mathematical Problems in Engineering

Krichanchai and MacCarthy [3] studied the needs of en-terprises to select suppliers to manage inventory +e in-dicators for selecting suppliers indicate that high-qualitysuppliers can bring greater benefits to the enterpriseIrmayanti [4] applied the analytic hierarchy process (AHP)method to deal with such problems in response to the factthat it is difficult for raw material suppliers to make deci-sions Sadrian and Yoon [5] and Pan [6] studied the single-objective linear programming modelrsquos supplier selectionproblem for the uncertain demand of suppliers Literature[7ndash9] proposed that when constructing the evaluation indexsystem criteria such as product design and improvement ofproduct sustainability should be considered Literature[10ndash12] proposed that flexibility criteria should be usedwhen selecting suppliers flexibility in response to changes inorders and uncertain demand Mummalaneni et al [13]aimed at the high-quality cooperative relationship of en-terprise suppliers and proposed that buyers and sellersstrengthen relationship building Chen et al [14] establisheda fuzzy multiattribute supplier selection model based on thetriangular fuzzy set theory Cakar and Cavus [15] used fuzzyTOPSIS to select the best dairy supplier Chakraborty et al[16] studied the application of the D-MARCOS method insupplier selection of the sustainable supply chain manage-ment system Zavadskas et al [17] used the FAHPmethod tostudy the purchasing suppliers of materials needed for theproduction of preinsulated pipes

Previous research is often carried out in a deterministicenvironment considering the supplierrsquos supply capacitydelivery date inventory and other constraints as a knownquantity At the same time the complexity and uncertaintyof the supplier are not considered and the potential risks ofthe supplier are ignored which is inconsistent with the actualsituation Most of the above methods stay in the theoreticalstage and have not been put into practice Based on theconditions during the internship period in a shipbuildingcompany in Shanghai China and on the basis of actualresearch we compared the existing supplier selectionmethods and aimed to choose the right one Table 1 showsthe characteristics of each method

Due to the extremely complexity and uncertainty ofshipbuilding suppliers and the lack of knowledge or data inthis field it is difficult to evaluate them with accuratenumbers So intuitionistic fuzzy numbers are used torepresent fuzziness and uncertainty Based on this on thebasis of the practical investigation of shipbuilding enter-prises during the internship of shipbuilding enterprisesaccording to the knowledge and experience and the actualneeds of supplier evaluation in shipbuilding enterprises thetransformation relationship between linguistic variablevalue and intuitionistic fuzzy set is established At the sametime a hybrid method namely SWARA and COPRAS isused to select shipbuilding suppliers +e weight of thesupplier index is determined by using the intuitionistic fuzzySWARA method +e ranking of suppliers is determined bythe intuitionistic fuzzy COPRAS method +e method

considers all kinds of uncertainties and evaluates the utilityand cost indicators of alternative suppliers Finally the ef-fectiveness and stability of the method are proved bycomparison and sensitivity analysis +erefore this methodis suitable for shipbuilding enterprises

3 The Intuitionistic Fuzzy MulticriteriaDecision-Making Method

31 Intuitionistic Fuzzy Sets

Definition 1 (see [18]) Let X be a nonempty set given amapping

fA X⟶ [0 1] times[0 1]

x↦ μA(x) ]A(x)( 1113857(1)

Among them 0le μA(x) + ]A(x)le 1 fA determines anintuitionistic fuzzy set of nonempty set X denoted as A

langx μA(x) ]A(x)rang|x isin X1113864 1113865 where μA(x) is a membershipfunction representing the membership degree of x tointuitionistic fuzzy sets A and ]A(x) is the nonmembershipfunction representing the nonmembership degree of x tointuitionistic fuzzy sets A Let πA(x) 1 minus μA(x) minus ]A(x)where πA(x) denotes the degree of hesitation or uncertainty+erefore the intuitionistic fuzzy number can also bedenoted as (μx ]x πx) and in this paper they are denoted as(μx ]x)

Definition 2 (see [19]) For intuitionistic fuzzy numbersα (μ ]) its score function and accuracy function aredefined as

S(α) μ minus ]

H(α) μ + ](2)

Among them S(α) isin [minus 1 1] and H(α) isin [0 1]

Definition 3 (see [20]) +e score function and function ofDefinition 2 are improved For an intuitionistic fuzzynumber α (μ ]) the improved score function and accu-racy function are as follows

Slowast(α)

S(α) + 12

Hlowast(α)

μ + ]2

(3)

Now Slowast(α) isin [0 1] and Hlowast(α) isin [0 1]

Definition 4 Let αj (μj ]j)(j 1 2 n) be a series ofintuitionistic fuzzy numbers ω (ω1ω2 ωn)T for thecorresponding weight vector and 1113936

nj1 ωj 1 ωj isin [0 1]

+en the algorithm formula of the intuitionistic fuzzyweighted average (IFWA) operator is as follows

Mathematical Problems in Engineering 3

IFWAw α1 α2 αn( 1113857 oplus nj1 ωjαj 1 minus 1113945

n

j11 minus μj1113872 1113873

ωj 1113945

n

j1]ωj

j⎛⎝ ⎞⎠ (4)

32 Intuitionistic Fuzzy SWARA Method +e stepwiseweight assessment ratio analysis (SWARA) method is a newmulticriteria decision-making method for evaluating stan-dard weights that was proposed by Kersuliene [21ndash24] +eSWARA method and the intuitionistic fuzzy set theory arecombined to become the intuitionistic fuzzy SWARAmethod +e steps are as follows

Step 1 Evaluation index ranking Each decision-makerexpresses the relative importance of each indicatoraccording to the corresponding intuitionistic fuzzynumber then uses equation (4) and the weight of thedecision-maker to obtain the intuitionistic fuzzyweighted arithmetic average operator of the indicatorand then uses equation (3) to find the score functionSlowast(Cj) of the indicator According to the score functionvalue of each indicator the indicators are ranked fromlarge to smallStep 2 +e relative importance correlation coefficientof each index sj(jge 2) is determined From the secondindex to the last index the difference between the scorefunction values of two adjacent indexes is taken as theimportance correlation coefficient sj(jge 2) which is

sj Slowast

Cjminus 11113872 1113873 minus Slowast

Cj1113872 1113873 among jge 2 (5)

Step 3 +e comparison coefficient is calculated +ecalculation formula is as follows

kj 1 j 1

sj + 1 jgt 1

⎧⎨

⎩ (6)

Step 4 +e relative weight factor is calculated +ecalculation formula is as follows

qj

1 j 1

qjminus 1

kj

jgt 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(7)

Step 5 +e final weight factor is calculated +e cal-culation is as follows

λj qj

1113936nk1 qk

(8)

33 Intuitionistic Fuzzy COPRAS Method +e complexproportional assessment method (complex proportionalassessment) that is the COPRAS method was introduced byZavadskas et al [25] +is method comprehensively con-siders different evaluation performance indicators and theircorresponding weights It combines each indicatorrsquos im-portance and utility to gradually make the alternative hi-erarchical sorting and evaluation and select the best planfrom them [2326ndash28] +e COPRAS method is combinedwith the intuitionistic fuzzy set to become the intuitionisticfuzzy COPRAS method +e steps are as follows

Step 1 According to equation (9) an intuitionisticfuzzy decision matrix R is established which is

R

r11 r12 r1n

r21 r22 r2n

rm1 rm2 rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

rij IFWAω(z(1)ij z

(2)ij middotmiddotmiddotz

(p)

ij )ω1lowastz(1)ij oplusω2lowastz

(2)ij oplus middotmiddotmiddotoplus

ωplowastz(p)ij (1minus 1113937

p

k1(1minus μ(k)ij )ωk 1113937

p

k1(](k)ij )ωk ) among

them z(k)ij (μ(k)

ij ](k)ij ) z(k)

ij (k 12 p) indicates thatwhen the alternative i corresponds to the index j theintuitionistic fuzzy number is evaluated by the k thexpert m is the number of alternatives and n is thenumber of evaluation indexes

Table 1 Comparison of supplier selection methods

Method Features

Analytic hierarchy process (AHP) Simple and practical qualitative and quantitative combination but more indicators easily lead to anincrease in the amount of calculation

BP neural network method Strong nonlinear mapping ability but need a large number of samples and modeling is difficult

Fuzzy set theory and method +e certainty of fuzzy problem is helpful to understand the uncertainty problem and has strongsubjectivity

Network analysis method (ANP) It can reflect the dependence between hierarchies and it is difficult to understand the relationshipbetween factors

TOPSIS method Full use of original data less information loss strong subjective factorsMathematical programming(MP) model Solving single-objective and multiobjective models more complex

Hybrid methods Combine a variety of methods to solve play the advantages of each method


Step 2 Equations (4) and (9) are used to obtain theweighted intuitionistic fuzzy decision matrix Y whichis

Y

y11 y12 y1n

y21 y22 y2n

ym1 ym2 ymn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (10)

Among them yi1 λ1ri1 (1 minus (1 minus μri1)λ1 (]ri1

)λ1) yin λnrn (1 minus (1 minus μrin

)λn (]rin)λn ) i isin 1 2

mStep 3 +e sum of the benefit index and cost index iscalculated +e number of indexes is n order T1

1 2 e shows benefit index setT2 e + 1 e + 2 n represents a set of cost indi-cators and then

β+i opluse

j1y

+ij i 1 2 m (11)

βminus i oplusn

je+1y

minusij i 1 2 m (12)

where y+ij indicates the benefit index value and yminus

ij

represents the cost indicator valueStep 4 +e relative importance valueQi(i 1 2 m) of each alternative is calculated andthe calculation formula is as follows

Qi Slowast β+i( 1113857 +

Smin lowast 1113936mi1 Slowast βminus i( 1113857

Slowast βminus i( 1113857 1113936

mi1 SminS

lowast βminus i( 1113857( 1113857 (13)

Among them Smin miniSlowast(βminus i) Slowast(β+i) is the score

function value of β+i and Slowast(βminus i) is the score functionvalue of βminus iStep 5+e utility degree value Ni of each alternative iscalculated as follows

Ni Qi

Qmaxtimes 100 i 1 2 m (14)

where Qmax MaxiQi According to the standard that Ni ofQmax is 100 the corresponding utility degree of suppliers ofother shipbuilding enterprises is calculated +e suppliers ofshipbuilding enterprises are ranked according to Ni valuefrom high to low+e higher value of Ni represents the idealalternative

4 Proposed Research Frameworks forAlternative Supplier

Because of the fluctuation of the market economy and theuncertainty and diversification of shipownersrsquo demand thisarticle discusses supplier selection for shipbuilding enter-prises from the perspective of intuitionistic fuzzy setsIntuitionistic fuzzy set can express the preference of deci-sion-makers from membership nonmembership and hes-itation It can better describe the shipbuilding companyrsquossupplier selection problemrsquos ambiguity and uncertainty An

intuitionistic fuzzy multicriteria decision-making methodframework is proposed to select shipbuilding enterprisesuppliers +is framework consists of 3 phases as follows

Phase 1 Decision-makers alternative suppliers andevaluation indicators are determined+e set of alternatives is A A1 A2 Am1113864 1113865 the setof evaluation indicators is C C1 C2 Cn1113864 1113865 and thecorresponding weight vector is λ (λ1 λ2 λn)T+e experts invited to evaluate alternative suppliers areE E1 E2 Ep1113966 1113967 and the corresponding weightvector is ω (ω1ω2 ωp)T Different weights areassigned to each expertrsquos evaluation results based ontheir educational background position and years ofexperiencePhase 2 +e weight of the evaluation index isdeterminedIn many MCDM problems one of the most criticalproblems is to determine the weight of the evaluationindex SWARA is a new weight extraction method in-troduced by et al [24] Compared with other effectiveweight evaluation methods based on the pairwisecomparison such as AHP or analytic network process(ANP) this method is neither complex nor time-con-suming and it does not need to evaluate the rankingcriteria too much Decision-makers are easy to partic-ipate in the weight determination process Each deci-sion-maker expresses his preference for the evaluationindex according to the corresponding intuitionistic fuzzynumber and then uses expert weight and intuitionisticfuzzy weighted arithmetic average operator to synthesizeeach evaluation indexrsquos importance Finally the scorefunction value of the intuitionistic fuzzy number cor-responding to each evaluation index is calculatedAccording to each indexrsquos score function value theweight of each index is determined +e weight of theindex is further applied to the intuitionistic fuzzy CO-PRAS method to rank the alternativesPhase 3 +e best shipbuilding enterprise supplier ischosen

For the multi-index decision-making problem of ship-building enterprises there is a dimensional inconsistency be-tween indicators Each indicator does not have a unifiedmeasurement standard so it is difficult to compare and thereare contradictions between goals It is precisely because of thecontradiction and dimensional inconsistency betweenmultipleindicators in the multi-index decision-making problemMultiple indicators cannot be merged into a single indicator+erefore in the process of decision analysis decision makersneed to consider a series of contradictory and interrelatedindicators and select the best option from the alternatives byusingmulti-indicator decision-makingmethod In this paper anew multi-index comprehensive evaluation method namelythe intuitionistic fuzzy COPRAS method is used to determinethe ranking of alternative suppliers and select the best ship-building supplier Figure 1 shows the flow chart of theintuitionistic fuzzy multicriteria decision-making framework


5 Case Analysis

51 Problem Description +e case study of this paper is ashipyard located in Shanghai China On the basis of practiceinvestigation in shipbuilding enterprises it is found thatshipbuilding enterprises need many outfitting parts paintwelding materials and mechanical and electrical materialsand there are also many suppliers to choose from Afterranking candidate suppliers different suppliers still havedifferent supply capabilities such as product price productquality delivery date and service level According to theactual situation of shipbuilding enterprises the selection ofsuppliers can be considered from the following five aspects

(1) Price and Cost +e purchasing cost is the highestcost of shipbuilding enterprises Shipbuilding en-terprises choose more suppliers and purchase moreproducts +erefore in supplier purchasing man-agement purchasing cost is generally strictly con-trolled Price and cost generally include the productprice freight cost and tariff if they are overseassuppliers

(2) Quality and Technology To preserve the safety of thefinished goods and their longevity after long-termusage the shiprsquos quality demands exquisite shipyardmanufacturing and high-quality supporting itemsfrom suppliers

(3) Response Speed and Supply Capacity In the ship-building supply chain the time of each link should be

strictly controlled and the materials can be deliveredon time according to the predetermined schedule Ifthe supplierrsquos product quantity is delayed too muchit will lead to a shortage of a part which may causethe whole production line to stop and affect theproduction efficiency

(4) Service Level Suppliers provide good service tocustomers especially in the procurement process ofcommunication In the process of shipbuilding thesupplierrsquos speed and attitude in dealing with theproblems of equipment installation and commis-sioning and the timeliness of after-sales service aftership delivery all belong to the service category +esupplier provides good service for customers es-pecially the communication in the procurementprocess

(5) Level of Risk Because of the increase in uncertaintythe risk level must also be considered It mainlyincludes supplier cooperation risk and capital risk Ifit is an overseas supplier it also includes the sup-plierrsquos geographical locationrsquos economic and politicalstability

+is research study uses shipbuilding enterprises thatwant to buy the same type of steel as an example +eshipyard selects three experienced decision-makers from thedepartment to evaluate steel suppliers All of them have beenengaged in supplier management of shipbuilding enterprisesfor more than 10 years+erefore the set of decision-makers

Phase 1 determine the decision experts alternative suppliers and evaluation indicators

Phase 2 intuitionistic fuzzy SWARA method is used to determine the weight of evaluationindexes

Phase 3 intuitionistic fuzzy COPRAS method is used to determine the ranking of alternativesuppliers

Step 1 determine alternative supplier set and evaluation index setStep 2 determine decision-makers set and their corresponding weights

Step 1 get the ranking of evaluation indexStep 2 determine the relative importance correlation coefficient of each indexStep 3 determine the comparison coefficient calculated for each indexStep 4 calculate the relative weight factor for each indexStep 5 determine the final weight for each index

Step 1 build intutionistic fuzzy decision matrixStep 2 build weighted intutionistic fuzzy decision matrixStep 3 calculate the sum of benefit and cost indexStep 4 calculate the relative importance of alternative suppliersStep 5 determine the rankings of alternative suppliers

Figure 1 Flow chart of the intuitionistic fuzzy multicriteria decision-making framework


is E E1 E2 E31113864 1113865 After the evaluation of suppliers by thethree decision-makers there are still five alternative steelsuppliers and the set of alternative suppliers isA (A1 A2 A3 A4 A5) +e set of supplier evaluation in-dexes is C C1 C2 C3 C4 C51113864 1113865 C1 represents quality andtechnology level C2 represents service level C3 representsresponse speed and supply capacity C4 represents risk leveland C5 represents price and cost Among them C1 C2 andC3 are benefit indicators and C4 and C5 are cost indicatorswhere the larger the index value of benefit indicators isbetter and the smaller the index value of cost indicator isbetter A management questionnaire about benefit type andcost type is established based on these five standards Toverify the management questionnairersquos scientific validity andindependence three experienced decision-makers are pro-vided the questionnaires separately to avoid being influ-enced by other experts when scoring When evaluating thetypes of benefit and cost indicators each expert gives theiropinions on shipbuilding enterprise suppliersrsquo selectioncriteria according to their expertise experience judgmentand relevant knowledge +e management questionnaire isbased on the statements in Tables 2 and 3

52 Algorithm Results

Phase 1 Decision-makers alternative suppliers andevaluation indicators are determinedIt can be seen from the above that the set of expertdecision-makers is E E1 E2 E31113864 1113865 the set of alter-native suppliers is A A1 A2 A3 A4 A51113864 1113865 and the setof evaluation indicators is C C1 C2 C3 C4 C51113864 1113865Expert decision-makers E contain 3 experts Due to thedifferent levels and experience of experts in order tomake the evaluation results more scientific and rea-sonable different weights are given to expertsaccording to their educational background positionand working years +e results are shown in Table 4According to Table 4 the weight of the decision-makerscan be obtained ω (ω1ω2ω3) (03404 03830

02766)Phase 2 +e weight of the evaluation index isdetermined+e three decision-makers expressed their preferencefor indicators according to the intuitionistic fuzzynumbers in Table 2 and then obtained Table 5according to Table 4 and equations (3) and (4)According to Table 4 score function value Slowast(Cj) isobtained which is sorted from large to small and afterthat Table 6 is obtained According to Table 6 theweight of the evaluation index can be obtained

λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)

Phase 3 +e priority of steel suppliers is determined

Table 7 is obtained according to Table 3 +en Table 8 isobtained according to equation (4) and Table 7 According to

equations (4) and (9) the weighted intuitionistic fuzzydecision matrix is obtained and the results are shown inTable 9 According to equations (11)ndash(14) we can get S+i Sminus iQi and Ni() and the results are shown in Table 10According to the relative importance value and effect degreevalue of the steel suppliers in Table 10 the importance ofsteel alternative suppliers for shipbuilding enterprises isranked as follows A1 gtA3 gtA4 gtA5 gtA2 so A1 is the bestsupplier It can be seen from Table 10 that the benefit value ofA1 ranks second but its cost value is the lowest so it ranksfirst comprehensively +e benefit value of A3 is the secondbut its cost value is high so it is the second which is in linewith the actual situation In order to select the best supplierthe value of the benefit index and cost index should beweighed comprehensively

53 Comparative Analysis In order to verify the effective-ness and rationality of the decision model the fuzzy TOPSISmethod [15 29] fuzzy CoCoSo method [30] and fuzzyMOORA method [31] are applied to the decision matrix (asshown in Table 9) +e risk ranking results of the fourmethods are shown in Table 11 According to Table 11 theTOPSIS method can be seen that A1 gtA3 gtA5 gtA4 gtA2 andthe rest are A1 gtA3 gtA4 gtA5 gtA2 which shows the effec-tiveness of this method

54 Sensitivity Analysis It can be seen from the above thatthere are five evaluation indexes for shipbuilding enterprisesto select steel suppliers quality and technical level (C1)service level (C2) response time and supply capacity (C3)risk level (C4) and price and cost (C5) In this section byexchanging each evaluation indexrsquos weight with the weightof another evaluation index the weight of other evaluation

Table 2 Linguistic terms for rating the importance of criteria

Linguistic terms IFNsExtremely important (EI) (090 005)Very important (VI) (080 015)Important (I) (065 030)Middle (M) (050 045)Unimportant (U) (035 060)Very unimportant (VU) (020 075)Extremely unimportant (EU) (010 090)

Table 3 Linguistic terms for rating the alternatives

Linguistic terms IFNsExtremely good (EG)extremely high (EH) (100 000)Very very good (VVG)very very high (VVH) (090 010)Very good (VG)very high (VH) (080 010)Good (G)high (H) (070 020)Medium good (MG)medium high (MH) (060 030)Fair (F)medium (M) (050 040)Medium bad (MB)medium low (ML) (040 050)Bad (B)low (L) (025 060)Very bad (VB)very low (VL) (010 075)Very very bad (VVB)very very low (VVL) (010 090)


indexes remains unchanged +en the relative importancevalue and utility value of alternative steel suppliers forshipbuilding enterprise are calculated S1 C1-C2 is scenario 1which means the weight of C1 is exchanged with that of C2

+e weight of other indicators remains unchanged Byanalogy there are a total of 10 scenarios namely S1 C1-C2S2 C1-C3 S3 C1-C4 S4 C1-C5 S5 C2-C3 S6 C2-C4 S7 C2-C5S8 C3-C4 S9 C3-C5 and S10 C4-C5 In each scenario the

Table 4 +e relative importance and weight value of decision-makers

No Working years Education level Position WeightsExpert 1 21 MSc Deputy minister 03404Expert 2 15 PhD Minister 03830Expert 3 26 BS Steel plate team leader 02766

Table 5 Index importance and its score function values

Index E1 E2 E3 Aggregated IFNs Score function value Slowast(Cj)

C1 VI I VI (07522 01956) 07783C2 I M M (05572 03920) 05826C3 I VI I (07175 02301) 07437C4 M U M (04471 05024) 04724C5 VI VI EI (08349 01107) 08621

Table 6 Weight values obtained by the intuitionistic fuzzy SWARA method

Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619

Table 7 +e ratings of the alternative suppliers

Supplier A1 A2 A3 A4 A5

Expert E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3C1 G VG G MG G MG VG VVG VG MG G G F MG MGC2 MG G MG F MG G VG G VG MG F MG MG MG FC3 VG G VG G G MG VG VG G VG G G VG G MGC4 L L L ML M ML VL M M MH ML ML M ML MC5 ML ML L M M ML L H MH MH L ML ML L ML

Table 8 Intuitionistic fuzzy aggregation decision matrix of steel supplier selection for shipbuilding enterprises

Index A1 A2 A3 A4 A5

C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)

Table 9 Weighted intuitionistic fuzzy aggregation decision matrix for shipbuilding enterprises to choose steel suppliers


C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)


relative importance and utility values of each supplier arecalculated Table 12 shows the relative relevance values of theten scenarios whereas Table 13 shows the utility values Inevery case supplier A1 comes out on top +e supplier issorted as A1 gtA3 gtA4 gtA5 gtA2 +erefore it can be con-cluded that the intuitionistic fuzzy set is a reliable tool toselect suitable suppliers for shipbuilding enterprises whichverifies the stability and effectiveness of the method andmodel

6 Conclusion

In recent years shipbuilding companiesrsquo selection of themost suitable suppliers has become an essential issue inshipbuilding sustainable supply chain management Sup-plier selection is a complex problem and issue for ship-building companies due to multi-index criteria and increasein uncertain information which is called uncertain multi-criteria decision-making (MCDM) problem A multicriteria

Table 10 Supplier evaluation results and ranking based on the intuitionistic fuzzy COPRAS method

Supplier β+i S+i βminus i Sminus i Qi Ni() Ranking

A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4

Table 11 Ranking by different methods

Supplier Proposed method TOPSIS CoCoSo MOORAA1 1 1 1 1A2 5 5 5 5A3 2 2 2 2A4 3 4 3 3A5 4 3 4 4

Table 12 Sensitivity analysis of rankings by Qi

Scenarios A1 A2 A3 A4 A5 SortS1 08986 07143 08648 07514 07503 A1 gtA3 gtA4 gtA5 gtA2S2 09049 07169 08683 07578 07518 A1 gtA3 gtA4 gtA5 gtA2S3 09071 07065 08586 07464 07444 A1 gtA3 gtA4 gtA5 gtA2S4 09051 07179 08739 07577 07469 A1 gtA3 gtA4 gtA5 gtA2S5 08984 07131 08685 07485 07427 A1 gtA3 gtA4 gtA5 gtA2S6 09090 07146 08683 07564 07482 A1 gtA3 gtA4 gtA5 gtA2S7 08965 07168 08767 07509 07402 A1 gtA3 gtA4 gtA5 gtA2S8 09045 07052 08652 07411 07326 A1 gtA3 gtA4 gtA5 gtA2S9 09064 07198 08734 07613 07519 A1 gtA3 gtA4 gtA5 gtA2S10 09142 07110 08794 07488 07325 A1 gtA3 gtA4 gtA5 gtA2

Table 13 Sensitivity analysis of rankings by Ni()



decision-making method based on the intuitionistic fuzzySWARA-COPRAS method is proposed to solve this prob-lem +is method has not been used to solve the problem ofsupplier selection in shipbuilding enterprises Intuitionisticfuzzy sets are an excellent way to deal with the uncertainty ofshipbuilding companiesrsquo suppliers Intuitionistic fuzzynumbers can be obtained from degrees of membershipnonmembership and hesitation which represent decision-makersrsquo preferences and better characterize the problemrsquosambiguity and ambiguity Decision-makersrsquo weight is de-cided objectively based on their skill experience judgmentand related knowledge which is closer to the truth of thedecision-making situation +e intuitionistic fuzzy SWARAapproach is used to determine the weights of the five in-dicators chosen by the shipbuilding companyrsquos suppliers+e intuitionistic fuzzy COPRAS approach is used to rankand evaluate the relative importance of different ship-building companies with the best one being chosen Finallythe example of shipbuilding enterprise of steel supplier basedin Shanghai China is considered and the steel suppliersrsquoranking is determined

Although the intuitionistic fuzzy multicriterion deci-sion-making method has piqued the interest of academicsboth at home and abroad and has yielded some results itsstudy is still in its infancy and requires more developmentand promotion In the future research we can focus on thefollowing directions First of all the SWARA method hassome limitations in determining the weight of supplierindicators It is based on actual data and has a high level ofsubjectivity thus it can be included in the subjectiveweighting At the same time the objective weight is intro-duced If the data authenticity is high the subjective weightis given a higher value If it cannot be determined it can take05 Secondly in sensitivity analysis some standard meth-odologies can be used to change the weight so as to test theeffectiveness and sensitivity of the method Last the intui-tionistic fuzzy multicriteria decision-making method canconsider intuitionistic triangular fuzzy number intuition-istic trapezoidal fuzzy number and the bipolar fuzzy sets torepresent the fuzziness and uncertainty At the same time itcan be combined with other MCDM methods to comparewith the results of this paper

Data Availability

+e data used to support this study are included within thearticle as Tables 2 to 13

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] J Chai J N K Liu and E W T Ngai ldquoApplication ofdecision-making techniques in supplier selection a systematicreview of literaturerdquo Expert Systems with Applications vol 40no 10 pp 3872ndash3885 2013

[2] A Reyes Avelina M Abraham and O B Elias ldquoA heuristicmethod for the supplier selection and order quantity

allocation problemrdquo Applied Mathematical Modelling vol 90no 2 pp 1130ndash1142 2021

[3] S Krichanchai and B L MacCarthy ldquo+e adoption of vendormanaged inventory for hospital pharmaceutical supplyrdquo 9eInternational Journal of Logistics Management vol 28 no 3pp 755ndash780 2017

[4] H Irmayanti ldquoRaw material supplier selection with analyticshierarchy process (AHP) methodrdquo IOP Conference SeriesMaterials Science and Engineering vol 879 no 1 Article ID012048 2020

[5] A A Sadrian and Y S Yoon ldquoA procurement decisionsupport system in business volume discount environmentsrdquoOperations Research vol 42 no 1 pp 14ndash23 1994

[6] A C Pan ldquoAllocation of order quantities among suppliersrdquoJournal of Purchasing and Materials Management vol 25no 2 pp 36ndash39 1989

[7] S C Ting and I ChoD ldquoAn integrated approach for supplierselection and purchasing decisionsrdquo Supply Chain Manage-ment An International Journalvol 13 no 2 pp 116ndash1272007

[8] 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

[9] H Fazlollahtabar and N Kazemitash ldquoGreen supplier se-lection based on the information system performance eval-uation using the integrated best-worst methodrdquo FactaUniversitatis Series Mechanical Engineering 2021

[10] S Chopra and PMeindl Supply ChainManagement StrategyPlanning and Operation PearsonPrentice Hall HobokenNJ USA Global edition 2001

[11] M Kumar P Vrat and R Shankar ldquoA fuzzy goal pro-gramming approach for vendor selection problem in a supplychainrdquo Computers amp Industrial Engineering vol 46 no 1pp 69ndash85 2003

[12] R Verma and M E Pullman ldquoAn analysis of the supplierselection processrdquo Omega vol 26 no 6 pp 739ndash750 1998

[13] V Mummalaneni K M Dubas and C N Chiang-nan ChaoldquoChinese purchasing managersrsquo preferences and trade-offs insupplier selection and performance evaluationrdquo IndustrialMarketing Management vol 25 no 2 pp 115ndash124 1996

[14] C-T Chen C-T Lin and S-F Huang ldquoA fuzzy approach forsupplier evaluation and selection in supply chain manage-mentrdquo International Journal of Production Economicsvol 102 no 2 pp 289ndash301 2006

[15] T Cakar and B Ccedilavus ldquoSupplier selection process in dairyindustry using fuzzy-topsis methodrdquo Operational Research inEngineering Sciences 9eory and Applications vol 4 no 1pp 82ndash98 2021

[16] S Chakraborty R Chattopadhyay and S Chakraborty ldquoAnintegrated D-MARCOS method for supplier selection in aniron and steel industryrdquo Decision Making Applications inManagement and Engineering vol 3 no 2 pp 49ndash69 2020

[17] E K Zavadskas Z Turskis Z Stevic and A MardanildquoModelling procedure for the selection of steel pipes supplierby applying fuzzy AHP methodrdquo Operational Research inEngineering Sciences 9eory and Applications vol 3 no 2pp 39ndash53 2020

[18] K T Atanassov ldquoMore on intuitionistic fuzzy setsrdquo Fuzzy Setsand Systems vol 33 no 1 pp 37ndash45 1989

[19] Z Xu ldquoMethods for aggregating interval-valued intuitionisticfuzzy information and their application to decision makingrdquoControl and Decision vol 22 no 2 pp 215ndash219 2007

[20] G-L Xu S-P Wan and X-L Xie ldquoA selection method basedon MAGDM with interval-valued intuitionistic fuzzy setsrdquo


Mathematical Problems in Engineering vol 2015 Article ID791204 13 pages 2015

[21] C Liu ldquoSupplier selection evaluation of shipbuilding enter-prises based on entropy weight and multi-attribute decisionmakingrdquo Proceedings of the Fifth International Forum onDecision Sciences pp 255ndash268 Springer Berlin Germany2018

[22] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 2 pp 626ndash6382017

[23] N Zarbakhshnia H Soleimani and H Ghaderi ldquoSustainablethird-party reverse logistics provider evaluation and selectionusing fuzzy SWARA and developed fuzzy COPRAS in thepresence of risk criteriardquo Applied Soft Computing vol 65no 1 pp 307ndash319 2018

[24] V Kersuliene E K Zavadskas and Z Turskis ldquoSelection ofrational dispute resolution method by applying new step-wiseweight assessment ratio analysis (SWARA)racionalaus gincusprendimo budo nustatymas taikant nauja kriteriju svoriunustatymo metoda pagrista nuosekliu laipsnisku poriniukriterijurdquo Journal of Business Economics and Managementvol 11 no 2 pp 243ndash258 2010

[25] E K Zavadskas Z Turskis and J Tamosaitiene ldquoMulticriteriaselection of project managers by applying grey criteriaprojektu valdytojo parinkimo daugiatikslio vertinimo mod-elisrdquo Technological and Economic Development of Economyvol 14 no 4 pp 462ndash477 2008

[26] A Roozbahani H Ghased and M Hashemy ShahedanyldquoInter-basin water transfer planning with grey COPRAS andfuzzy COPRAS techniques a case study in Iranian CentralPlateaurdquo Science of the Total Environment vol 726 no 7Article ID 138499 2020

[27] Y Zheng Z Xu Y He and H Liao ldquoSeverity assessment ofchronic obstructive pulmonary disease based on hesitantfuzzy linguistic COPRAS methodrdquo Applied Soft Computingvol 69 no 1 pp 60ndash71 2018

[28] D Schitea M Deveci M Iordache K Bilgili I Z Iordacheand I Iordache ldquoHydrogen mobility roll-up site selectionusing intuitionistic fuzzy sets based WASPAS COPRAS andEDASrdquo International Journal of Hydrogen Energy vol 44no 16 pp 8585ndash8600 2019

[29] M Gul and M F Ak ldquoA comparative outline for quantifyingrisk ratings in occupational health and safety risk assessmentrdquoJournal of Cleaner Production vol 196 no 9 pp 653ndash6642018

[30] U Alptekin K C Bulent and A Topal ldquoLocation selectionfor logistics center with fuzzy SWARA and CoCoSomethodsrdquo Journal of Intelligent amp Fuzzy Systems vol 38no 4 pp 4693ndash4709 2020

[31] D Rahim and Y Samuel ldquoA hybrid decision-making ap-proach based on FCM and MOORA for occupational healthand safety risk analysisrdquo Journal of Safety Research vol 71no 12 pp 111ndash123 2019


(neither support nor opposition) In 1986 Bulgarian scholarKT Atanassov proposed the concept of intuitionistic fuzzysets Intuitionistic fuzzy sets use two scales (degree ofmembership and nonsubordination) to characterize ambi-guity simultaneously expressing support opposition andneutrality and can describe the natural attributes of ob-jective phenomena in a more detailed and comprehensivemanner In view of the fluctuation of the market economyand the uncertainty of shipownerrsquos demand this paperproposes a new intuitionistic fuzzy multicriteria decision-making method based on the SWARA (stepwise weightassessment ratio analysis) and COPRAS (complex propor-tional assessment) method In this paper the intuitionisticfuzzy SWARA-COPRAS method is used for the followingreasons (1) Intuitionistic fuzzy sets are a good solution Itcan express decision-makers preferences from three aspectsmembership degree nonmembership degree and hesitationdegree and can more describe the vagueness and uncertaintyof the problem (2) +e method is simple easy to under-stand and easy to implement (3) Transaction costs are lowand decision-makers have more opportunities to set stan-dard priorities

+e contributions of this paper are as follows

(i) Taking into account the vacillation of shipbuildingmarket economy and the uncertainty and diversityof shipownersrsquo demand the corresponding rela-tionship between the linguistic value of expertevaluation and intuitionistic fuzzy set is established

(ii) In the supplier index selection of shipbuilding en-terprises the risk index is included In the selectionof suppliers most of them focus on the cost qualityand service level and rarely take the risk intoaccount

(iii) +e intuitionistic fuzzy SWARA-COPRAS methodis established and applied to a new field supplierselection of shipbuilding enterprises

+e structure of this article is as follows Section 2provides a literature review Section 3 details the intui-tionistic fuzzy multicriteria decision-making method Sec-tion 4 introduces the framework of the intuitionistic fuzzymulticriteria method In Section 5 a shipbuilding companybased in Shanghai China is taken as an example and thealgorithms comparative analysis and the sensitivity analysisshow that the method is effective and stable Section 6 givesthe conclusions of this article

2 Literature Review

21 Supplier Management in Shipbuilding Enterprises In theera of information digitization the essence of the need forcommunication between enterprises and timely exchange ofdemand information drives a new mode of cooperationnamely supply chain management (SCM) With the rapiddevelopment of global economic integration and the in-creasing external competition environment of shipbuildingenterprises the global market competition is becomingmoreandmore intense and SCMhas become an important means

for shipbuilding enterprises to improve their core compe-tition Compared with other manufacturing industriesshipbuilding enterprise supply chain management has itsown uniqueness Shipbuilding has the characteristics ofcustom production +e main impetus of creation comesfrom the end-client transport proprietor which is thegenuine interest chain of ship pulling +ere are many co-operative enterprises in the whole supply chain nodethrough mutual cooperation the whole shipbuilding supplychain management process can be completed

+e supply chain management process of shipbuildingventures with center shipbuilding endeavors as the principlebody is firmly identified with the necessities of shipownersand furthermore includes different materials and hardwareand their providers Shipbuilding is a typical large-scalemanufacturing and assembly industry of on-demand pro-duction +e materials and resources required range fromsupporting equipment plates and profiles to coatings ce-ment and cabin furniture Its suppliers are all over theworld and the number can reach thousands and the ma-terials or equipment provided by these suppliers for ship-building enterprises directly affect the structural design andproduction schedule of ship products As a result changes inessential design technology and schedule information inthe shipbuilding process must be communicated to keysuppliers in a timely manner giving them enough time toalter supply times and inventory levels avoiding resourceloss due to cost increases In addition shipowners will alsopropose to the core shipbuilding enterprises to supply to thedesignated suppliers which requires the core shipbuildingenterprises to establish a good communication environmentbetween shipowners and suppliers to ensure the mutualbenefit of the three parties

22 Shipbuilding Enterprise Supplier Selection MethodRelated research shows that an important part of estab-lishing win-win SCM is to choose agile competitive andcompatible partners namely suppliers +e problem ofsupplier selection for shipbuilding enterprises is one of themain problems of shipbuilding supply chain managementAt present the methods for supplier selection can be roughlydivided into four categories [1] (1) Multiattribute decision-making methods include analytic hierarchy process prior-itize the organization of ranking improvement evaluationmethod network analysis method and approximate idealsolution sorting method (TOPSIS) (2) Mathematical pro-gramming model includes stochastic planning goal plan-ning nonlinear programming data envelopment analysis(DEA) linear programming and multiobjective planning(3) Artificial intelligence technology includes genetic algo-rithm grey system theory neural network rough set theorycase-based reasoning (CBR) particle swarm algorithm antcolony algorithm and fuzzy set theory (FTS) (4) Combi-nation (mixed) model includes AHP+GP AHP+LPAHP+FTS and DEA+MOP Avelina et al [2] studied theparticle swarm optimization (PSO) algorithm and differ-ential evolution (DE) algorithm for supplier selection andorder quantity allocation decision-making problems









fA X⟶ [0 1] times[0 1]

x↦ μA(x) ]A(x)( 1113857(1)




S(α) μ minus ]

H(α) μ + ](2)



Slowast(α)

S(α) + 12

Hlowast(α)

μ + ]2

(3)







n

j11 minus μj1113872 1113873

ωj 1113945

n

j1]ωj

j⎛⎝ ⎞⎠ (4)



sj Slowast


Cj1113872 1113873 among jge 2 (5)


kj 1 j 1

sj + 1 jgt 1

⎧⎨

⎩ (6)


qj

1 j 1

qjminus 1

kj

jgt 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(7)


λj qj

1113936nk1 qk

(8)



R

r11 r12 r1n

r21 r22 r2n

rm1 rm2 rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

rij IFWAω(z(1)ij z


(p)




p


p


them z(k)ij (μ(k)

ij ](k)ij ) z(k)



Method Features









Y

y11 y12 y1n

y21 y22 y2n

ym1 ym2 ymn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (10)






β+i opluse

j1y

+ij i 1 2 m (11)

βminus i oplusn

je+1y



ij





mi1 SminS

lowast βminus i( 1113857( 1113857 (13)



Ni Qi









5 Case Analysis





















λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References











































fA X⟶ [0 1] times[0 1]

x↦ μA(x) ]A(x)( 1113857(1)




S(α) μ minus ]

H(α) μ + ](2)



Slowast(α)

S(α) + 12

Hlowast(α)

μ + ]2

(3)







n

j11 minus μj1113872 1113873

ωj 1113945

n

j1]ωj

j⎛⎝ ⎞⎠ (4)



sj Slowast


Cj1113872 1113873 among jge 2 (5)


kj 1 j 1

sj + 1 jgt 1

⎧⎨

⎩ (6)


qj

1 j 1

qjminus 1

kj

jgt 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(7)


λj qj

1113936nk1 qk

(8)



R

r11 r12 r1n

r21 r22 r2n

rm1 rm2 rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

rij IFWAω(z(1)ij z


(p)




p


p


them z(k)ij (μ(k)

ij ](k)ij ) z(k)



Method Features









Y

y11 y12 y1n

y21 y22 y2n

ym1 ym2 ymn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (10)






β+i opluse

j1y

+ij i 1 2 m (11)

βminus i oplusn

je+1y



ij





mi1 SminS

lowast βminus i( 1113857( 1113857 (13)



Ni Qi









5 Case Analysis





















λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References





































n

j11 minus μj1113872 1113873

ωj 1113945

n

j1]ωj

j⎛⎝ ⎞⎠ (4)



sj Slowast


Cj1113872 1113873 among jge 2 (5)


kj 1 j 1

sj + 1 jgt 1

⎧⎨

⎩ (6)


qj

1 j 1

qjminus 1

kj

jgt 1

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(7)


λj qj

1113936nk1 qk

(8)



R

r11 r12 r1n

r21 r22 r2n

rm1 rm2 rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

rij IFWAω(z(1)ij z


(p)




p


p


them z(k)ij (μ(k)

ij ](k)ij ) z(k)



Method Features









Y

y11 y12 y1n

y21 y22 y2n

ym1 ym2 ymn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (10)






β+i opluse

j1y

+ij i 1 2 m (11)

βminus i oplusn

je+1y



ij





mi1 SminS

lowast βminus i( 1113857( 1113857 (13)



Ni Qi









5 Case Analysis





















λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References





































Y

y11 y12 y1n

y21 y22 y2n

ym1 ym2 ymn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (10)






β+i opluse

j1y

+ij i 1 2 m (11)

βminus i oplusn

je+1y



ij





mi1 SminS

lowast βminus i( 1113857( 1113857 (13)



Ni Qi









5 Case Analysis





















λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References




































5 Case Analysis





















λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References








































λ λ1 λ2 λ3 λ4 λ5( 1113857 (02159 01797 02086

01619 02339)(15)



















Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References












































Index sj kj qj λj

C5 08621 mdash 1 1 02339C1 07783 00838 10838 09227 02159C3 07437 00346 10346 08918 02086C2 05826 01611 11611 07681 01797C4 04724 01102 11102 06919 01619






C1 (07432 01534) (06417 02568) (08466 01000) (06691 02296) (05684 03309)C2 (06417 02568) (06014 02958) (07664 01304) (05643 03349) (05745 03248)C3 (07664 01304) (06752 02237) (07763 01211) (07387 01580) (07170 01767)C4 (02500 06000) (05399 04590) (03892 04954) (04774 04202) (04638 04357)C5 (03618 05259) (04741 04255) (05563 03252) (04307 04506) (03465 05362)



C1 (02543 06671) (01988 07457) (03329 06083) (02124 07278) (01659 07876)C2 (01684 07833) (01524 08034) (02300 06935) (01387 08216) (01424 08171)C3 (02616 06538) (02091 07317) (02683 06438) (02442 06805) (02315 06966)C4 (00455 09206) (01181 08816) (00767 08925) (00997 08690) (00960 08741)C5 (00997 08604) (01396 08188) (01731 07689) (01235 08299) (00947 08643)



6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References





































6 Conclusion




A1 (0542203416) 06003 (0140707921) 01743 09046 100 1A2 (0462804384) 05122 (0241207218) 02597 07165 7921 5A3 (0624102716) 06763 (0236506863) 02751 08690 9607 2A4 (0487304069) 05402 (0210907212) 02448 07568 8366 3A5 (0450304483) 05010 (0181607556) 02130 07500 8291 4










Data Availability




References






































Data Availability




References




































SupplierSelectionofShipbuildingEnterprisesBasedon ...sets. Intuitionistic fuzzy sets use two scales...

Documents

Transcript of SupplierSelectionofShipbuildingEnterprisesBasedon ...sets. Intuitionistic fuzzy sets use two scales...