FUZZY CLUSTERING MODELING AND EVALUATION OF ...clustering algorithm or subtractive clustering (Chiu...

FUZZY CLUSTERING MODELING AND EVALUATION OFSURFACE INTERACTIONS AND EMULSIONS OF SELECTED

WHEAT PROTEIN COMBINED TO IOTA-CARRAGEENAN ANDGUM ARABIC SOLUTIONS

MAHMOUD ABU-GHOUSH1,5, MURAD SAMHOURI2, EMAD YASEEN3

and THOMAS HERALD4

1Clinical Nutrition and Dietetics Department

2Department of Industrial EngineeringThe Hashemite University

PO Box 330156, Zarqa 13133, The Hashemite Kingdom of Jordan

3Research and DevelopmentSolae LLC, St. Louis, MO

4Food Science InstituteKansas State University

220 Call Hall, Manhattan 66506, KS

Accepted for Publication March 6, 2008

ABSTRACT

Gums and proteins are valuable ingredients with a wide spectrum ofapplications. Surface properties (surface tension, interfacial tension, emul-sion activity index [EAI] and emulsion stability index [ESI]) of 4% deami-dated wheat protein (DWP) in a combination with iota-carrageenan (IC)(0.05, 0.1 and 0.5%) or gum arabic (GA) (0.5, 1 and 5%) were investigated.The results showed that the addition of IC to 4% DWP significantly increasedthe surface tension, interfacial tension, EAI and ESI, whereas the addition ofGA to 4% DWP significantly increased the surface tension and decreased theinterfacial tension and EAI (except at 5% of GA). In addition, a fuzzy-basedclustering model was used to predict the surface properties of the DWP.The fuzzy model achieved accuracies of (97%, 90%, 97% and 75%) forpredicting (EAI, ESI, surface tension and interfacial tension), respectively.This approach can be applied to predict many other parameters and proper-ties in the food industry.

5 Corresponding author. TEL: 962-7-85799274; FAX: 962-5-3903350; EMAIL: [email protected]

Journal of Food Process Engineering •• (2008) ••–••. All Rights Reserved.© Copyright the AuthorsJournal Compilation © 2008 Wiley Periodicals, Inc.DOI: 10.1111/j.1745-4530.2008.00324.x

1

mailto:[email protected]

PRACTICAL APPLICATIONS

The surface properties (surface tension, interfacial tension, emulsionactivity index and emulsion stability index) of wheat protein (DWP) in com-bination with iota-carrageenan or gum arabic were investigated. In addition,subtractive clustering-based fuzzy models for predicting the surface propertiesof DWP was constructed. This modeling can be used as an indicator ofusefulness of fuzzy clustering in such a system which directly can be used asa tool by the food processors to produce a high quality beverage product.

INTRODUCTION

The wheat industry has done little to promote the use of wheat protein inbeverages. Wheat proteins can alternate and compete with other proteinsbecause of its functional and dietary benefits. Soluble wheat protein, such asMidsol WPI 2100 from Midwest Grain, Inc. (Atchison, KS), can be used inbeverage production as an alternative for casein and soy proteins. Withoutresearch to promote the effectiveness of wheat protein in beverages, the wheatindustry will lose out. The food industry and academia have expressed aninterest in gum–protein mixtures because of their contributions to stability andfunctionality. The interaction between proteins and polysaccharides in manyfood systems are responsible for structural, mechanical and physicochemicalproperties of emulsions, foams and gels (Igoe 1982; Dallgleish 1996). Thegum–protein interaction may play a more significant role in the food systemcompared to the single contribution of the individual polymer (Dickinson1998). Proteins improve the surface properties of food systems by forming aprotective steric barrier around oil droplets, whereas gums improve the stericstabilizing properties through forming a thick secondary layer on the outsideof protein (Dickinson 1998). Bárcenas et al. (2003) found that the addition ofhydrocolloids to wheat dough would increase its stability and reduce themixing time. This modification could be related to the hydrocolloids–proteininteractions. Probably the most effective interaction between hydrocolloidsand wheat protein is ionic. Electrostatic effects of the polysaccharides do notexplain all the interactions. The configuration of the molecules and the avail-ability of charged groups also may be important. The carboxylate groups onthe acidic heteropolysaccharides (e.g., xanthan) are mainly associated with thea-amino, e-amino group of the protein. The actual strength of interactions isrelated to the number and distribution of these sites as well as the overallcharge of the protein. The hydrogen bonding also may play an important roleand the hydrophilic and hydrophobic interactions may occur between the

2 M. ABU-GHOUSH ET AL.

hydrocolloids and proteins. Thus, a fundamental understanding of behavior,mechanism and interaction between gums and proteins in beverage systems ilimited.

The hydrocolloids (gums) have the ability to control both the rheologyand texture throughout the stabilization of emulsions, suspensions, foams andstarch gelatinization (Rosell et al. 2001). Wheat protein–polysaccharide inter-actions should be well known in order to formulate ingredients in a moreaccurate way. Iota-carrageenan (sulfated hydrocolloid) (IC) and gum arabic(amphiphilic polysaccharides) (GA), formed from galactose, rhamnose, ara-binopyranose, glucouronic acid and 4-metheyl glucouronic acid, are carbohy-drates of relatively high molecular weight when compared with simple sugar.GA is the most commonly used biopolymer emulsifier in beverage production(Tan 1998). The two types of macromolecules are both important in control-ling the rheology and the stability of the food system. Interactions of thesebiopolymers with proteins in the food system determine structure–propertyrelationships in foods. The decrease in surface tension by proteins andamphiphilic macromolecules is usually caused by the surface active entity ofthe macromolecules, adsorption and unfolding of the macromolecule at theinterface, and the adsorbed segments rearrangement at the fluid interface(Dickinson 2003).

Fuzzy logic and fuzzy inference system (FIS) are effective techniques forthe identification and modeling of complex nonlinear systems. Fuzzy logic isparticularly attractive because of its ability to solve problems in the absence ofaccurate mathematical models. The prediction of surface properties of DWP incombination with IC or GA is considered as a complex system, so using theconventional technology to model these properties results in significant dis-crepancies between simulation results and experimental data. Thus, thiscomplex nonlinear system fits within the realm of the fuzzy logic technique.

Modeling and identification of food properties and processing has beenthe subject of many researchers in the food engineering field. A classificationof wheat by visible and near-infrared reflectance from a single kernel wasintroduced by Delwiche and Massie (1996). Their classification model accu-racy ranged from 65% for SRW wheat to 92% for SWH. Welch et al. (2003)presented a genetic neural network model of flowering time control inArabidopsis thaliana. Their results included tracking a novel, temperature-dependent exchange in transition order exhibited by two mutants whose dupli-cation is not possible by usual crop simulation methods. An artificial neuralnetwork prediction of amino acid levels in feed ingredients was introduced byRoush and Cravener (1997). Two types of neural networks and linear regres-sion were evaluated for predicting amino acid levels in corn, wheat, soy beanmeal, meat, bone meal and fish meal. Samhouri et al. (2007) found that theneuro-fuzzy modeling technique (i.e., adaptive neuro-fuzzy inference system

FUZZY CLUSTERING MODELING 3

[ANFIS]) can be used to achieve very satisfactory prediction accuracy (about98%) in a model color mayonnaise system. Also, very satisfactory predictionaccuracy (about 96%) was achieved by applying the neuro-fuzzy modelingtechnique (i.e., ANFIS) in predicting the emulsion stability and viscosity of agum–protein emulsifier in a model mayonnaise system (Abu Ghoush et al.2008).

The main motivation behind this work is to promote the effectiveness ofusing wheat protein concentrate in combinations with IC and GA in beverageproduction. Therefore, the main aims of this study were: (1) evaluate the effectof gums (IC and GA) and proteins (wheat protein), in combination, on thesurface and emulsion properties of a fluid food system; and (2) model, identifyand predict the surface properties of wheat protein–gum interactions using afuzzy clustering model. The fuzzy prediction models for the surface propertiesof wheat protein in a biphasic system with IC and GA solutions will open theopportunity for the untapped beverage market. The benefits will reach theproducers, consumers, processors, communities and agriculture. Also, fuzzymodeling will give the opportunity for the manufacturers to know the optimumconditions for formulating high quality stable products.

MATERIALS AND METHODS

Soluble wheat protein Midsol WPI 2100 (DWP) was obtained fromMidwest Grain, Inc. IC and GA were obtained from TIC Gums, Inc. (Belcamp,MD).

Emulsion Preparation and Evaluation

Preparation of Emulsions. IC (0.05, 0.1 and 0.5%) or GA (0.5, 1 and5%) were prepared in buffer by stirring the dispersions vigorously for 30 minat room temperature, while heating at 50C until the solution became clear.Four percent of wheat protein concentrate/IC and GA were made based on theprocess patented by Chen et al. (1989).

Emulsion Evaluations. Emulsion activity index (EAI) and emulsionstability index (ESI) for all the previously mentioned combinations weredetermined by using a turbidimeteric method developed by Pearce andKinsella (1978).

The surface and interfacial tensions were determined by a Fisher SurfaceTensiometer (model 21; Indiana, PA). The force acting on the ring was mea-sured as it was moved upward for an air-solution dispersion interface, and as


it was moved downward for an oil-solution interface. The equilibrium time forsteady state surface tension measurements was 30 min. All tests were carriedout in triplicate.

Statistical Analysis

A two-way factorial classification in complete randomized design wasused to design the experiments in this study. Data were analyzed using SASsoftware (version 8.2, SAS Institute Inc., Cary, NC). Three batches of solu-tions were produced for each treatment. Analysis of variance and meansseparations were calculated by the general linear model procedure. Compari-sons among treatments were analyzed using Fisher Least Significant Differ-ence, and treatment means were considered significant at P < 0.05.

Fuzzy-based Clustering Model

Clustering of numerical data forms the basis of many classification andsystem-modeling algorithms. The purpose of clustering is to identify naturalgroupings of data from a large data set to produce a concise representation ofa system’s behavior (Jang and Gulley 2000). A cluster is a set of objects thatare more similar to each other than to objects from other clusters. Variousclustering algorithms have been developed recently. These include fuzzyC-means algorithm (Bezdek 1974), mountain-clustering algorithms (Yagerand Filev 1994) and a more computationally efficient version of mountainclustering algorithm or subtractive clustering (Chiu 1994).

Fuzzy subtractive clustering (FSC) is a fast, one-pass algorithm for esti-mating the number of clusters and the cluster centers in a set of data (Chiu1994). Subtractive clustering is based on a measure of the density of datapoints in the feature space (Jang et al. 1997). The idea is to find regions in thefeature space with the high densities of data points. The point with the highestnumber of neighbors is selected as center for a cluster. The data points withina pre-specified fuzzy radius are then removed (subtracted), and the algorithmlooks for a new point with the highest number of neighbors. This continuesuntil all the data points are examined.

The subtractive clustering algorithm starts by considering a collectionof K data points specified by m-dimensional vectors uk, k = 1, 2, . . . , K.Without loss of generality, the data points are assumed normalized. Since eachdata point is a candidate for a cluster center, a density measure at data point ukis defined as

Draj

kk j

K u u= −

−

( )⎛⎝⎜

⎞⎠⎟=

∑exp2 21

(1)


Hence, a data point will have a high density value if it has many neigh-boring data points. Only the fuzzy neighborhood within the radius ra, contrib-utes to the density measure.

After calculating the density measure for each data point, the point withthe highest density is selected as the first cluster center.

Let uc1 be the point selected and Dc1 its density measure. Next, the densitymeasure for each data point uk is revised by the formula

′ = − ⋅ −−

( )⎛⎝⎜

⎞⎠⎟

D D Du u

k k c1k c1exprb 2

2(2)

Therefore, the data points near the first cluster center uc1 will havesignificantly reduced density measures, thereby making the points unlikely tobe selected as the next cluster center. The constant rb, defines a neighborhoodto be reduced in density measure. It is normally larger than ra to preventclosely spaced cluster centers, typically rb = 1.5ra.

After the density measure for each point is revised, the next cluster centeruc2 is selected and the density measures are revised again. The process isrepeated until a sufficient number of clusters are generated (Jantzen 1998).When applying subtractive clustering to a set input/output data, each of thecluster centers represents a rule. To generate rules, the cluster centers are usedas the centers for the premise sets in a singleton type of rule base.

An important advantage of using a subtractive method to find rules is thatthe resultant rules are more tailored to the input data than they are if they areFIS generated without clustering. This reduces the problem of combinatorialexplosion of rules when the input data has a high dimension (the dreaded curseof dimensionality) (Jang and Gulley 2000).

We selected the FSC approach to determine cluster centers using param-eter ra = 14. This value is the maximum distance between any two pointswithin the same cluster, yet less than the distance between any two points fromdifferent clusters where each point belongs. The multiplier Sqsh = 1.25 is thedefault squash factor value of MATLAB 7.0 (Mathworks, Natick, MA).

The criteria for cluster center consideration are based on acceptance andrejection ratios.Acceptance ratio can be determined by fractions of the potentialfirst cluster center, above which another data point will be accepted. Rejectionratio is the condition to reject a data point to be a cluster center, which is obtainedfrom fractions of the potential first cluster center, below which a data point willbe rejected as a cluster center. We chose 0.5 as the acceptance ratio (which isthe default value from MATLAB 7.0) for the first cluster center. We chose therejection ratio (h) between 0.15 and 0.5 to derive other cluster centers. Theresulting rejection ratios from various cluster centers were used to compare and


evaluate the component classification. The procedure for grouping 35 data pointclusters {X1, X2, X3, . . . , Xn = 35} in the training set is described in thefollowing as an example of calculating subtractive clusters:(1) Compute the initial potential value of each data point (Pi) by using the

following equation:

P eia x x

j

ni j= − −

=∑

2

1

(3)

where a = 4/ra2; || . || is the Euclidean distance; and ra is a positiveconstant representing a normalized neighborhood data radius.Any point that falls outside this encircling region will have little influenceon the potential point. The point with the highest potential value is selectedas the first cluster center. This tentatively defines the first cluster center.

(2) A point is qualified as the first center if its potential value (P(1)) is equal tothe maximum of initial potential value (P(1)*):

P P xi i1 1( ) ( )= ( )( )* max (4)

(3) Define a threshold d as the decision to continue or stop the cluster centersearch. This process will continue if the current maximum potentialremains greater than d.

δ = ( )⋅( )reject ratio potential value of the first cluster center

where the rejection ratio (h) used in this work is 0.15–0.5, and P(1)* is thepotential value of the first cluster center.

(4) Remove the previous cluster center from further consideration.(5) Revise the potential value of the remaining points according to the

equation

P P P ei i kx xi k= − − −* β

2

(5)

where xk* is the point of the kth cluster center, Pk* is its potential value andb = 4/1.25 (sqsh * ra).

(6) For the point having the maximum potential value, calculate the accep-tance ratio. If this value is greater than the predefined constant (0.5), thepoint is accepted to be the next cluster center. Otherwise, compute therejection ratio. If the rejection ratio is greater than the predefined threshold(h = 0.15–0.5), this point is accepted.

This procedure is repeated to generate the cluster centers until themaximum potential value in the current iteration is equal to or less than the


threshold d. After applying subtractive clustering, we get different clustercenter numbers from 35 training patterns depending on different rejectionratios. We used these different cluster center numbers to compare and evaluatethe surface properties classification.

RESULTS AND DISCUSSION

Surface and Interfacial Tensions of Deamidated WheatProtein–Gum Solutions

As shown in Fig. 1, the addition of 0.05, 0.1 and 0.5% IC significantlyincreased the surface tension of 4% deamidated wheat protein (DWP) by 4.4,6.7 and 22.8%, respectively, whereas addition of 0.5, 1 and 5% GA signifi-cantly increased the surface tension of 4% DWP by 2.2, 3.7 and 7.7%, respec-tively. The highest achieved surface tension was when the IC had been addedat 0.5% to the wheat protein solution. The effect of the polysaccharide inincreasing the rate of surface tension by the protein is consistent with substan-tial net attractive interaction between IC and DWP. As illustrated in Fig. 2, theinterfacial tension of the 4% DWP significantly increased by addition of 0.1and 0.5% IC by 19.5 and 310.9%, respectively, whereas addition of 0.5, 1 and5% GA significantly decreased the interfacial tension by 62.7, 52.2 and 51.2%,respectively. The increase or the decrease in the interfacial tension within eachpolysaccharide-protein combination was due to the effect of the net attractiveinteraction and the degree of the adsorption and unfolding at the interface. Thedecrease in surface tension by proteins and amphiphilic hydrocolloids usuallycauses the surface active entity to diffuse from the bulk phase to the subsurfacelayer. This step is followed by the adsorption and unfolding of the macro-

0

10

20

30

40

50

Dynes/cm

Treatments

DWP

DWP-0.05% IC

DWP-0.1% IC

DWP-0.5% IC

DWP-0.5% GA

DWP-1% GA

DWP-5% GA

e c ba

d bcd

FIG. 1. COMPARISON BETWEEN IC AND GA ON THE SURFACE TENSION OF 4% DWP.BARS WITH THE SAME LETTERS ARE NOT SIGNIFICANTLY DIFFERENT AT P < 0.5

IC, iota-carrageenan; GA, gum arabic; DWP, deamidated wheat protein.


molecule at the interface and finally the adsorbed segments rearrange at thefluid interface. In addition to lowering the interfacial tension, amphiphilicmacromolecules can form continuous viscoelastic films at the interface vianon-covalent intermolecular interactions (Dickinson 2003; Singh et al. 2003).

EAI and ESI of DWP–Gum Solutions

As given in Fig. 3, the EAI of 4% DWP significantly increased withaddition of 0.05, 0.1 and 0.5% IC by 5.2, 10.7 and 38.2%, respectively,whereas EAI of 4% DWP significantly decreased with addition of 0.5 and 1%GA by 21.7 and 18.8%, respectively, and significantly increased by addition of

0

2

4

6

8

10

12

14

Dynes/cm

Treatments

DWP

DWP-0.05% IC

DWP-0.1% IC

DWP-0.5% IC

DWP-0.5% GA

DWP-1% GA

DWP-5% GA

ccb

a

e dd

FIG. 2. COMPARISON BETWEEN IC AND GA ON INTERFACIAL TENSION OF 4% DWP.BARS WITH THE SAME LETTERS ARE NOT SIGNIFICANTLY DIFFERENT AT P < 0.5

IC, iota-carrageenan; GA, gum arabic; DWP, deamidated wheat protein.

0

100

200300

400

500

600

m2g-1

Treatments

DWP

DWP-0.05% IC

DWP-0.1% IC

DWP-0.5% IC

DWP-0.5% GA

DWP-1% GA

DWP-5% GA

d c b

a

f e

c

FIG. 3. COMPARISON BETWEEN IC AND GA ON THE EMULSION ACTIVITY INDEX OF4% DWP. BARS WITH THE SAME LETTERS ARE NOT SIGNIFICANTLY DIFFERENT

AT P < 0.5IC, iota-carrageenan; GA, gum arabic; DWP, deamidated wheat protein.


5% GA by 5.4%. The ESI of 4% DWP increased by addition of 0.05, 0.1 and0.5% IC by 711.6, 876.2 and 891.1%, respectively. The ESI of 4% DWP wasnot significantly changed with addition of 0.5 and 1% of GA but decreased byaddition of 5% GA by 33.7% as shown in Fig. 4. Interactions between the twopolymers could be segregative or associative. For instance, for GA at lowconcentration solutions, the system is stable and proteins and polysaccharidesare co-soluble. Upon increasing concentration, the system becomes unstabledepending of the type of interaction. In this case, biopolymer mixtures tend tosegregate (Tolstoguzov 1991; Grinberg and Tolstoguzov 1997). This trend isusually attributed to repulsive interactions between polymer segments. Segre-gation leads to a reduction of the local concentration of one of the polymersnear the second one because of a decrease of conformational entropy ofmacromolecules at an interface. In the case of IC, an associative state may beobserved due to interaction between the two biopolymers (protein and gum).At high concentration solutions, the system becomes stable. The polysaccha-ride molecules may adsorb onto protein, even bridging between several proteinmolecules. The gum additions increase the stability of emulsions by the for-mation of a polysaccharide network that prevents the fat globules from coa-lescence. This could be because of the formation of a matrix within the fluidphase, especially in the presence of protein that can form a second protectivelayer surrounding the fat globules (Prakash et al. 1990).

Fuzzy Clustering-based Prediction of Surface Propertiesof Wheat Protein

Clustering Data Preparation. Generating a subtractive clustering-based FIS requires dividing the training data into two matrices: (1) An input

0

100

200

300

400

500

Time (hr)

Treatments

DWP

DWP-0.05% IC

DWP-0.1% IC

DWP-0.5% IC

DWP-0.5% GA

DWP-1% GA

DWP-5% GA

c

ba a

cd cd d

FIG. 4. COMPARISON BETWEEN IC AND GA ON THE EMULSION STABILITY INDEX OF4% DWP. BARS WITH THE SAME LETTERS ARE NOT SIGNIFICANTLY DIFFERENT

AT P < 0.5IC, iota-carrageenan; GA, gum arabic; DWP, deamidated wheat protein.


matrix that contains all the input values to be used in training the fuzzy system.This input matrix should contain values for solution type and solution propor-tion%. Actually, 34 data points of these inputs were selected as given inTable 1. These points were then gathered into one matrix called “input

TABLE 1.TRAINING DATA MATRIX USED TO BUILD THE FUZZY MODEL OF SURFACE

PROPERTIES USING SUBTRACTIVE CLUSTERING

(a) Inputs (b) Outputs

Solution type Solutionproportion %

EAI ESI Surfacetension

Interfacialtension

10 0 422 42.1 40.2 4.210 0 419.4 43.3 42 310 0 417.8 42.5 40.3 310 0 422.6 44.3 40 310 0 423.1 40.1 40.2 2.510 0.05 433.4 36.9 42.2 2.910 0.05 437.6 328 43 3.110 0.05 442.9 316.2 39.1 3.210 0.05 437.6 385.9 42 2.410 0.05 436 326.8 42.4 2.910 0.1 456.8 400.8 41.2 2.110 0.1 457.3 381.2 40.5 2.910 0.1 454.4 413.2 42.1 310 0.1 451 451.2 43.7 4.110 0.1 451 451.2 43 3.310 0.5 516.8 436.2 49.5 12.210 0.5 516.3 409.5 50.5 13.210 0.5 516.8 409.9 48.5 12.710 0.5 516.6 406.6 48.5 12.510 0.5 516.3 403.3 50 1220 0.5 331 37.5 41.1 1.120 0.5 313.2 45.7 41.8 120 0.5 312.7 30.9 41.1 1.220 0.5 312.7 32.5 41.2 1.220 0.5 334.9 37.7 41.1 1.620 1 267.8 38.6 40.3 1.520 1 285.9 41.3 41 2.120 1 250.1 30.5 41.9 2.420 1 305.4 36.9 42.7 1.320 1 278.2 38.8 42.3 1.220 5 366.1 28.4 42.9 1.520 5 328.9 27.7 43.9 220 5 341.5 27.9 44 1.620 5 318.4 28.3 43.2 120 5 358.8 27.7 43.4 1.1

EAI, emulsion activity index; ESI, emulsion stability index.


matrix”; and (2) an output matrix that contains all the output values to be usedin training the fuzzy system. This output matrix should contain values for EAI,ESI, Surface Tension and Interfacial Tension. Thirty-four output data points,corresponding to the selected input points, were given in Table 2 (i.e., valida-tion table), and gathered into one matrix called “output matrix.” The remainingseven input/output data points, which are different from the training data, wereused for validation purposes.

Generating FIS for Surface Properties. The subtractive clusteringalgorithm estimates the cluster centers in a set of data. It assumes each datapoint is a potential cluster center and calculates a measure of the likelihoodthat each data point would define the cluster center, based on the density ofsurrounding data points. The algorithm:

(1) selects the data point with the highest potential to be the first clustercenter;

(2) removes all data points in the vicinity of the first cluster center (as deter-mined by radii), in order to determine the next cluster and its centerlocation; and

(3) iterates on this process until all of the data are within radii of a cluster center.

The radii variable is a vector of entries between 0 and 1 that specifies acluster center’s range of influence in each of the data dimensions, assuming thedata fall within a unit hyperbox. Small radii values generally result in findinga few large clusters. Good values for radii are usually between 0.2 and 0.5. Inthis article, a value of 0.8 for all the radii was chosen. This resulted in sameaccuracy and speed with less numbers of membership functions (MFs).

A special MATLAB function, built-in in the Fuzzy Logic Toolbox, wasused to generate the FIS. This function extracts a set of rules that model thedata behavior. This rule-extraction method first uses the subtractive clusteringcenters and clusters to determine the number of rules and antecedent MFs andthen uses linear least squares estimation to determine each rule’s consequentequations. This MATLAB function returned an FIS structure that contains a setof fuzzy rules to cover the feature space.

The least squares method of this function works on the consequent part ofFIS, especially on the generated fuzzy rules. This function minimizes thenumber of inference rules, but it uses large numbers of MFs. This complicatesthe fuzzification process only, but it simplifies the inference and defuzzifica-tion process, which has more impact on the computational time. The FIS,generated depending on the subtractive clustering, has a Sugeno-type infer-ence, with a weighted-average defuzzification method. Five bell-shaped MFsfor all inputs were used, some of them coincident, and are shown for each thetwo inputs (solution type and solution proportion%) in Fig. 5.


TAB

LE

2.T

HE

PRE

DIC

TIN

GFU

ZZ

YC

LU

STE

RIN

G-B

ASE

DM

OD

EL

FOR

SUR

FAC

EPR

OPE

RT

IES

OF

WH

EA

TPR

OT

EIN

Solu

tion

type

Solu

tion

prop

.%E

AI

act.

EA

Ipr

ed.

EA

Ier

ror

%E

SIac

t.E

SIpr

ed.

ESI

erro

r%

Surf

.te

nsio

nac

t.

Surf

.te

nsio

npr

ed.

Surf

.te

nsio

ner

ror

%

Inte

r.te

nsio

nac

t.

Inte

r.te

nsio

npr

ed.

Inte

r.te

nsio

ner

ror

%

100

418

421

0.8

4043

5.9

3841

63.

63.

1412

.810

0.05

433

438

136

127

922

.739

427.

52.

12.

938

100.

145

645

40.

438

642

08.

745

425.

84

3.08

2310

0.5

517

517

043

641

35.

350

491.

412

.112

.53.

320

0.5

331

321

334

378.

541

410

1.7

1.22

2820

125

227

79.

832

3715

.542

420

2.3

1.7

2620

537

734

39

2728

2.9

4344

0.7

11.

4444

Ave

rage

Perc

ent

Err

or3.

49.

93.

225

EA

I,em

ulsi

onac

tivity

inde

x;E

SI,e

mul

sion

stab

ility

inde

x.


Only five rules were found by the optimization algorithm to be necessaryto generate a highly efficient FIS that predicts the surface properties withoutany loss of accuracy, and with much less computational time. The final FISstructure is shown in Fig. 6. The final fuzzy models for predicting the surfaceproperties of wheat protein are given as surface plots of the outputs (i.e., EAI,ESI, surface tension and interfacial tension) against the inputs (i.e., solutiontype and solution proportion%) as illustrated in Figs. 7–10, respectively.

Model Validation. The fuzzy prediction models for surface properties ofwheat protein were validated by selecting a certain number of data points(7 points), different and independent from the other 34 points used for fuzzymodel training. Each validation data point (i.e., solution type and solutionproportion%), given in Table 2, was fed into the system, and then the predictedsurface properties (i.e., EAI, ESI, surface tension and interfacial tension) werecompared to the actual values of these properties. The average percent errorsin the modeling of surface properties are given in Table 2, and are as follows:3.5% for EAI, 10% for ESI, 3% for surface tension and 25% for interfacialtension.

10 11 12 13 14 15 16 17 18 19 200

0.5

1

SolutionType

Deg

ree

of m

embe

rshi

p

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

SolutionProportion%

Deg

ree

of m

embe

rshi

p

Final MF for Input(Solution Type)5 MF, 4 coincident

Final MF for Input(Solution Proportion%)5 MF, 2 coincident

FIG. 5. FINAL MF OF INPUTS FOR THE SURFACE PROPERTIES PREDICTION MODELUSING SUBTRACTIVE CLUSTERING-BASED ALGORITHM

MF, membership functions.


CONCLUSIONS

In this article, surface properties (surface tension, interfacial tension, EAIand ESI) of DWP in combination with IC or GA were investigated. In addition,subtractive clustering-based fuzzy models for predicting the surface propertiesof wheat protein were constructed. The following conclusions can be drawnfrom the previously mentioned analysis:

(1) The surface tension was significantly increased by the addition of IC andGA at various increasing concentrations, and the highest was achievedwhen the IC had been added at 0.5% to the wheat protein solution. At thesame time, the interfacial tension was significantly increased by increas-ing IC concentrations, while the interfacial tension was significantlydecreased by increasing GA concentrations. This could be because of thesubstantial net attractive interaction between the gum types and DWP.

(2) The addition of IC to DWP significantly increased EAI and ESI, whereasthe addition of GA to DWP significantly increased the EAI (except at 5%

System subfuz: 2 inputs, 4 outputs, 5 rules

SolutionType (5)

SolutionProportion% (5)

f(u)

EAI (5)

f(u)

ESI (5)

f(u)

SurfaceTension (5)

f(u)

InterfacialTension (5)

subfuz

(sugeno)

5 rules

FIG. 6. FIS FOR SURFACE PROPERTIES PREDICTION USING SUBTRACTIVECLUSTERING-BASED OPTIMIZATION ALGORITHM

FIS, fuzzy inference system.


FIG. 7. A FUZZY MODEL (SURFACE PLOT) OF EAI AS FUNCTION OF INPUTS(SOLUTION PROPORTION% AND SOLUTION TYPE)

EAI, emulsion activity index.

FIG. 8. A FUZZY MODEL (SURFACE PLOT) OF ESI AS FUNCTION OF INPUTS (SOLUTIONPROPORTION% AND SOLUTION TYPE)

ESI, emulsion stability index.


FIG. 9. A FUZZY MODEL (SURFACE PLOT) OF SURFACE TENSION AS FUNCTION OFINPUTS (SOLUTION PROPORTION% AND SOLUTION TYPE)

FIG. 10. A FUZZY MODEL (SURFACE PLOT) OF INTERFACIAL TENSION AS FUNCTIONOF INPUTS (SOLUTION PROPORTION% AND SOLUTION TYPE)


of GA), while the ESI was not significantly changed (except at 5% of GA).This trend is usually attributed to interactions between polymer segments.These interactions could be segregative or associative.

(3) FSC-based models achieved an average prediction error of wheat proteinsurface properties of 10%. The prediction accuracies are considered sat-isfactory when compared to previous work, and the fuzzy model wascapable of modeling the surface properties efficiently except for the inter-facial tension where the error was a bit high (i.e., 25%). The present studyshows that fuzzy clustering is a technique that can be used efficiently topredict the food properties. It is believed that this approach can be appliedto predict many other parameters and properties in the food industry. Thecapability of the fuzzy predictions models for the surface properties per-mitted the quantification of EAI, ESI, surface tension and interfacialtension to be studied in all types of emulsions (e.g., milk products, bev-erages). Computer vision shows promise for the online prediction ofsurface properties in biphasic system.

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