research article predicting the mechanical properties of...

Research ArticlePredicting the Mechanical Properties of ViscoseLycra KnittedFabrics Using Fuzzy Technique

Ismail Hossain12 Imtiaz Ahmed Choudhury1 Azuddin Bin Mamat1

Abdus Shahid3 Ayub Nabi Khan4 and Altab Hossain5

1Department of Mechanical Engineering Faculty of Engineering University of Malaya Kuala Lumpur Malaysia2Department of Textile Engineering Faculty of Engineering Daffodil International University 102 Sukrabad Mirpur RoadDhaka 1207 Bangladesh3Department of Textile Engineering Dhaka University of Engineering and Technology Gazipur Bangladesh4BGMEA University of Fashion and Technology (BUFT) Dhaka Bangladesh5Department of Nuclear Science amp Engineering Military Institute of Science and Technology Dhaka Bangladesh

Correspondence should be addressed to Ismail Hossain ismailpabyahoocom

Received 21 November 2015 Accepted 13 April 2016

Academic Editor Katsuhiro Honda

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

The main objective of this research is to predict the mechanical properties of viscoselycra plain knitted fabrics by using fuzzyexpert system In this study a fuzzy prediction model has been built based on knitting stitch length yarn count and yarn tenacityas input variables and fabric mechanical properties specially bursting strength as an output variable The factors affecting thebursting strength of viscose knitted fabrics are very nonlinear Hence it is very challenging for scientists and engineers to createan exact model efficiently by mathematical or statistical model Alternatively developing a prediction model via ANN and ANFIStechniques is also difficult and time consuming process due to a large volume of trial data In this context fuzzy expert system (FES)is the promising modeling tool in a quality modeling as FES can map effectively in nonlinear domain with minimum experimentaldata The model derived in the present study has been validated by experimental data The mean absolute error and coefficientof determination between the actual bursting strength and that predicted by the fuzzy model were found to be 260 and 0961respectively The results showed that the developed fuzzy model can be applied effectively for the prediction of fabric mechanicalproperties

1 Introduction

Knitting is one of the main fabric manufacturing methodsamong the knitting weaving and nonweaving in the textilemanufacturing Basically knit fabric is formed by intermesh-ing yarn loops with each other in wale and course directionsThe quality of fabrics is considered a big issue in the globaltextile and apparel market The demand of knitted fabricespecially viscose knitted fabric is increasing rapidly due totheir unique quality characteristics such as elasticity drapewrinkle resistance comfort softness and easy-care proper-ties over woven fabrics Viscose knitted fabrics are very popu-lar for apparel wears such as T-shirts shirts sweaters blousesunderwear casual wear active wear and sportswear because

of their distinctive quality characteristics as compared towoven fabrics [1ndash5]

The bursting strength however is one of the mostimportant mechanical properties among all the viscose plainknitted fabrics qualities Knitted fabrics are not just renderingforces in the vertical and perpendicular directions but alsothey are exposed tomultiaxial forces during dyeing finishingand usage Testing tensile and tearing strength in the waleand coarse directions in knitted fabrics are not suitablebecause of the structural properties hence testing burstingstrength turns out to be extremely important particularly forknitted fabrics before manufacturing Generally the burstingstrength test is conducted to evaluate the fabricrsquos capability towithstand multiaxial stresses without breaking off [1 4 6 7]

Hindawi Publishing CorporationAdvances in Fuzzy SystemsVolume 2016 Article ID 3632895 9 pageshttpdxdoiorg10115520163632895

2 Advances in Fuzzy Systems

Basically strength of fabrics depends on starting fabricforming materials such as yarn properties and fabric densityThe literature review revealed that various studies have beenreported on the factors affecting the bursting strength ofknitted fabric including yarn type yarn count yarn tenacityyarn breaking elongation yarn breaking strength yarn twistyarn evenness fabrics GSM fabric wale and courses knittingstitch length cover factor tightness factors and relaxationtreatment [1 4 6ndash8]

Moreover all these factors affecting the bursting strengthof knitted fabrics are nonlinear and interactive with otherHence it poses a great challenge for scientists and engineersto develop effectively an exact model based on mathematicaland statistical techniques [2 9] This is ascribed to the factthat both mathematical and statistical models often fail tocapture the nonlinear relationship between inputs and out-puts [10]

On the other hand the intelligent systems such asartificial neural network (ANN) and adaptive neuroinferencesystem (ANFIS) models which have the ability to model innonlinear domain have been applied by few researchers inthe previous research for predicting the bursting strengthof knitted fabrics Jamshaid et al applied ANFIS model topredict the bursting strength of plain knitted fabrics as afunction of yarn tenacity knitting stitch length and fabricGSM [1] Ertugrul and Ucar applied intelligent techniquenamely ANN and ANFIS models for the prediction ofbursting strength of the knitted fabrics using yarn strengthyarn elongation and fabric GSM as input variables [6] Unalet al presented ANN model for the prediction of burstingstrength as a function of yarn strength yarn count yarnevenness yarn twist yarn elongation and fabric wales andcourses [7] Bahadir et al used ANNmodel for the predictionof bursting strength of knitted fabrics [8] Zeydan studiedANN model for the prediction of woven fabric strength [11]However ANN and ANFIS models need large amounts ofnoisy input-output data for model parameters optimizationwhich are challenging labor intensive and time consumingprocesses to collect from the textile knitting industries [1 29] In addition ANN does not tell the core logic based onwhich decisions can be taken [10]

In this regard fuzzy expert system (FES) is found to bethe scientific and engineering solution for quality modelingas FES provides reliable prediction outcome with smallexperimental data in nonlinear and ill-defined textile domain[2 9] Moreover a fuzzy model is more reasonable cheaperin design cost and much easier to apply in comparisonto other models Furthermore fuzzy logic is used to solveproblems in which descriptions of behavior and observationsare imprecise vague and uncertain [2 9 10]

The key purpose of this work is to construct fuzzy intel-ligent model for predicting the bursting strength of viscoselycra plain knitted fabrics as a function of knitting stitchlength yarn count and yarn tenacity which is not reportedin the published literature

2 Materials and Method

21 Fuzzy Expert System The artificial intelligence fuzzyexpert system is a structure of multivalued logic and an

Fuzzifier

Crisp input Rule based

Inference engine

Crisp output

Defuzzifier

Figure 1 Fundamental unit of a fuzzy expert system [2 15]

extension of crisp logic derived from fuzzy mathematical settheory developed by Zadeh in 1965 [9 12 13] In crisp logicsuch as binary logic variables are true or false black or whiteand 1 or 0 If the set under investigation is 119860 testing of anelement 119909 using the characteristics function 119909 is expressed asfollows

120583119860 (119909) =

1 if 119909 isin 119860

0 if 119909 notin 119860(1)

A fundamental fuzzy logic unit comprises a fuzzifier a fuzzyrule base an inference engine and a defuzzifier as shown inFigure 1 [2 14 15]

Fuzzifier Fuzzifier is the first block in the fuzzymodeling thatconverts all numeric inputs-outputs into fuzzy sets withina range from 0 to 1 such as low medium and high byusingmembership functions [12]There are different forms ofmembership function such as triangle trapezoid and Gaus-sian [16] Amongnumerousmembership functions the trian-gular shaped membership function is the simplest and mostfrequently applied which is defined as follows [2]

120583119860 (119909 119886 119887 119888) =

119909 minus 119886

119887 minus 119886 119886 le 119909 le 119887

119888 minus 119909

119888 minus 119887 119887 le 119909 le 119888

0 otherwise

(2)

In this case the edge of the variablersquos interval may berepresented with linear S-shaped and Z-shaped membershipfunctions described respectively as follows

(i) S-shaped membership functions are

120583S (119909 119886 119887) =

1 119909 le 119886

119887 minus 119909

119887 minus 119886 119886 le 119909 le 119887

0 119909 ge 119887

(3)

(ii) Z-shaped membership functions are

120583Z (119909 119886 119887) =

0 119909 le 119886

119909 minus 119886

119887 minus 119886 119886 le 119909 le 119887

1 119909 ge 119887

(4)

Advances in Fuzzy Systems 3

In (2)ndash(4) 119909 is the input and output variables 119886 119887 and 119888are the coefficient of membership functions for the explainedinput and output variables

The Fuzzy Rule Base The fuzzy rules which are inferred fromexpert knowledge and experience are generally articulatedby if-then statements that narrate the input variables in theantecedent part and output variables in the consequent part[2 9] Besides fuzzy rules are the heart of the fuzzy logicexpert system which determines the input-output relation-ship of the model [9 10] The fuzzy rule base can be dividedinto two classes namely theMamdani and Sugeno [12 17]

Mamdani Rules Both of the antecedent and conse-quence parts are in fuzzy set form

Sugeno Rules The antecedent part is in the form of afuzzy set and the consequence part is made up by alinear equation or constant

As an expressionwhen a fuzzymodelwith two inputs andone output is involved then development of fuzzy inferencerules can be presented as follows

Mamdani Rule If 1199091 is 1198601 and 1199092 is 1198602 then 119910 is 1198621Sugeno Rule If 1199091 is 1198601 and 1199092 is 1198602 then 119910 = 1198870 +11988711199091 + 11988721199092

where 1199091 1199092 and 119910 are linguistic variables 1198601 1198602 and1198621 are the consequent fuzzy numbers that represent thelinguistic states and 1198870 1198871 and 1198872 are linear equation para-meters

Inference Engine The fuzzy inference engine is basically acontrol mechanism which performs vital role in the fuzzymodeling due to its ability to generate human decisionmaking and deduce control actions by applying the obviousknowledge in the rule base to the task-specific data to appearat some solution or conclusion [2 18] Mamdani suggestedthe application of a minimum operation rule as a fuzzy infer-ence function For three-inputs and single-output fuzzymod-eling fuzzy inference method is mathematically expressed asfollows [18]

120572119894= 120583119860119894(SL) and 120583119861119894 (YC) and 120583119862119894 (YT)

119894 = 1 2 119899

(5)

120583119862 (BS) =

119899

⋃

119894=1

[120572119894and 120583119862119894(BS)] (6)

where 120572119894is the weighting factor as a measure of the contribu-

tion of 119894th rule to the fuzzy control action and 120583119860119894 120583119861119894 120583119862119894

and 120583119862are the membership functions associated with fuzzy

sets 119860119894 119861119894 119862119894 and 119862 respectively

Defuzzifier Defuzzifier is the important and last block (unit)of fuzzy modeling Basically the conclusion of the inferenceengine is the fuzzy output Finally among different defuzzifi-cation methods the center of gravity method is adopted here

to convert the fuzzy inference output into a nonfuzzy value 119911in the following form for the distinct case [2 18]

119911 =sum119899

119894=1120583119894(119887119894)

sum119899

119894=1120583119894

(7)

where 119887119894is the position of the singleton in 119894th universe and 120583

119894

is the membership function of 119894 rule

22 Prediction Performance Measure The prediction accu-racy of the developed model has been investigated accordingto the global prediction error such as mean absolute error(MAE) and coefficient of determination (1198772) The formula-tions of those accuracy measures are given below

MAE = 1

N

119894=119873

sum

119894=1

(

10038161003816100381610038161003816119864a minus 119864p

10038161003816100381610038161003816

119864atimes 100)

1198772= 1 minus (

sum119894=119873

119894=1(119864a minus 119864p)

2

sum119894=119873

119894=1(119864a minus 119864M)

2)

(8)

where 119864a is actual result 119864p is predicted result 119864M is meanvalue and119873 is number of patterns

The coefficient of determinations (1198772) compares the accu-racy of the model to that of accuracy of a trivial benchmarkmodel The mean absolute error (MAE) gives the deviationbetween the predicted and experimental values and it isrequired to reach zero [2]

23 Development of Fuzzy Prediction Model For develop-ment of fuzzy prediction model three knitting variables suchas knitting stitch length (SL) yarn count (YC) and yarntenacity (YT) have been used as input variables and burstingstrength of knitted fabrics as output variable These knittingvariables have been exclusively selected as they influence thefabric bursting strength considerably A fuzzy logic Toolboxfrom MATLAB (version 7100) was used to develop theproposed fuzzy model of bursting strengthThe constructionof fuzzy modeling for bursting strength has been depicted inFigure 2

For fuzzification four possible linguistic subsets namelyvery low (VL) low (L) medium (M) and high (H) forinput variables SL and YC and three convenient linguisticsubsets namely low (L)medium (M) and high (H) for inputvariable YT were chosen in such a way that they are evenlyspaced and cover up the entire input spaces Ten outputfuzzy sets (Levels 1 to 10) (where 119871 = Level) are consideredfor fabric bursting strength (BS) so that the fuzzy expertsystem can map small changes in bursting strength with thechanges in input variables In this study the triangular shapedmembership functions are used for input-output variablesbecause of their accuracy Moreover a Mamdani max-mininference approach and the center of gravity defuzzificationmethod have been applied in this work Selection of thenumber of membership functions and their initial values isbased on the system knowledge and experimental conditions[2] There is a level of membership for each linguistic word


Input 1Stitch length (27ndash30)

Input 2Yarn count (24ndash36)

Input 3Yarn tenacity (1525ndash1575)

Rule 2 if (SL is L) and (YC is H) and(YT is L) then (BS is L2)

Rule 1 if (SL is VL) and (YC is H)and (YT is L) then (BS is L3)

Rule 23 if (SL is M) and (YC is VL) and (YT is M) then (BS is L9)

Rule 24 if (SL is H) and (YC is M)and (YT is H) then (BS is L6)

OutputBursting strength

Defuzzification

Aggregation

The nonfuzzy inputs areconverted to fuzzy numbers by membership function

All rules are evaluated in parallel using fuzzy reasoning

The results of the rules are combined and defuzzified

The result is nonfuzzynumber

Figure 2 Schematic diagram of fuzzy modeling for bursting strength [9]

that applies to that input variable Fuzzification of the usedfactors is made with the aid of the following functions

SL (1198941) =

1198941 27 le 119894

1le 30

0 otherwise

YC (1198942) =

1198942 24 le 119894

2le 36

0 otherwise

YT (1198943) =

1198943 1525 le 119894

3le 1575

0 otherwise

BS (1199001) =

1199001 270 le 119900

1le 460

0 otherwise

(9)

where 1198941 1198942 and 119894

3are the first (SL) second (YC) and

third (YT) input variables respectively and 1199001is the output

variable (BS) showing in (9)The triangular shaped membership functions for the

fuzzy variables namely stitch length (SL) yarn count (YC)and yarn tenacity (YT) and bursting strength (BS) have beencreated using fuzzy logic Toolbox from MATLAB software(version 7100) and are shown in Figures 3ndash6

The coefficients of membership functions for the fuzzyinference system (FIS) parameters are shown in Table 1

Conceptually there could be 4 times 4 times 3 = 48 fuzzy rulesas input variable SL having 4 linguistic levels YC having 4linguistic levels and YT having 3 linguistic levels Howeverin order to make the fuzzy expert system simpler only 24fuzzy rules have been formed based on expert knowledge and

VL HL M

27 28 285 29 295 3275Input variable ldquoSLrdquo

0

05

1

Figure 3 Membership function of input variable ldquoSLrdquo

VL HL M

24 28 30 32 34 3626Input variable ldquoYCrdquo

0

05

1

Figure 4 Membership function of input variable ldquoYCrdquo

previous experience [9] Some of the rules are presented inTable 2

To demonstrate the fuzzification process linguisticexpressions and membership functions of stitch length (SL)yarn count (YC) and yarn tenacity (YT) obtained from


HL M

153 1535 154 1545 155 1555 156 1565 157 15751525Input variable ldquoYTrdquo

0

05

1

Figure 5 Membership function of input variable ldquoYTrdquo

L1 L2 L3 L4 L5 L6 L7 L8 L9 L10

300 320 340 360 380 400 420 440 460280Output variable ldquoBSrdquo

0

05

1

Figure 6 Membership function of output variable ldquoBSrdquo

Table 1 Coefficients of membership functions for FIS parameter ofBS

Linguistic variables Type Coefficients ()119886 119887 119888

Level 1 Z-shaped 250 270 mdashLevel 2 Triangular 250 270 290Level 3 Triangular 270 290 310Level 4 Triangular 290 310 330Level 5 Triangular 310 330 350Level 6 Triangular 330 350 370Level 7 Triangular 350 370 390Level 8 Triangular 370 390 410Level 9 Triangular 390 410 435Level 10 Triangular 410 435 460

Table 2 Fuzzy inference rules

Rules number Input variables Output variableSL YC YT BS

1 VL H L Level 32 L H L Level 2

10 L L M Level 511 M L M Level 6

23 M VL M Level 924 H M H Level 6

the developed rules and above formula (9) are presented asfollows

120583119871 (SL) =

1198941minus 27

28 minus 27 27 le 119894

1le 28

29 minus 1198941

29 minus 28 28 le 119894

1le 29

0 1198941ge 29

(10a)

120583119871 (SL) =

0

27+005

275+1

28+ sdot sdot sdot +

005

285+0

29 (10b)

120583119871 (YC) =

1198942minus 24

28 minus 24 24 le 119894

2le 28

32 minus 1198942

32 minus 28 28 le 119894

2le 32

0 1198942ge 32

(11a)

120583119871 (YC) =

0

24+05

26+1


05

30+0

32 (11b)

120583119872 (YT) =

1198943minus 1525

155 minus 1525 1525 le 119894

3le 155

1575 minus 1198943

1575 minus 155 155 le 119894

3le 1575

0 1198943ge 1575

(12a)

120583119872 (YT)

= 0

1525+004

1535+

1


06

1565+

0

1575

(12b)

In defuzzification stage the membership functions (120583) ofthe rules are calculated for each rule by (3) To comprehendfuzzification an example is considered For crisp input SL =28mm YC = 28Ne and YT = 155 gtex the rule 10 is firedThe firing weighting factor 120572 of the one rule is calculated by(4) and found as

12057210= min (120583

119871 (SL) 120583119871 (YC) 120583119872 (YT))

= min (1 1 1) = 1(13)

Consequently according to (5) the membership function forthe conclusion reached by rules 10 is obtained as follows

12058310 (BS) = min 1 120583

1198715 (BS) (14)

Haghighat et al have cited that in many circumstances for asystem whose output is a fuzzy set it is essential to aggregatethe fuzzy sets into a single fuzzy set by aggregation method[12] Finally using (7) and (14) with Table 1 and Figure 6 thecrisp output of bursting strength is found to be 330 kPa

3 Experimental Work for the Validation ofFuzzy Model

31 Fabric Knitting and Heat Setting In this research total12 viscoselycra blended plain fabrics samples were knittedaccording to Table 3 knitted fabric variables on Pailung single


Table 3 Knitted fabric variables and their level

Process parameters Unit Level1 2 3 4

Stitch length mm 27 28 29 30Yarn count Ne 24 30 34Yarn tenacity gtex 1525 155 1575

Figure 7 Circular knitting machine (APS Textile Bangladesh)

jersey circular knitting machine (Figure 7) having 30 inchesdiameter 20 gauges (needlesinch) and 90 yarn feedersThe jersey knitted fabric was prewetted on the paddingmangle using 2 gL wetting detergent (Feloson NOF) and1 gL lubricating agent (Kappavon CL 1 gL) and then heatsetting was conducted on the pin stenter finishing machineat a temperature of 200∘C for 45 seconds of curing time

32 Fabric Processing and Testing The fabrics samples weresubjected to semibleached at 90∘C for 40min in a sampledyeing machine using anticreasing agent (Kappavon CL1 gL) sequestering agent (Sirrix 2UD 05 gL) wetting agent(Felosan NOF 1 gL) soda ash (25 gL) hydrogen peroxide50 (1 gL) and stabilizing agent (02 gL) Then the fabricssamples were washed with proper rinsing and finally treatedwith acetic acid (1 gL) and peroxide killing agent (02 gL)for neutralizing and peroxide killing respectively Afterbleaching the fabric samples were dried in an open stenterand compacted properly After production all the fabricssamples were conditioned on a flat surface first for at least 24hours prior to testing under standard atmospheric conditionsat relative humidity (65 plusmn 2) and temperature (20 plusmn 2)∘CThen the bursting strength (kPa) of each sample was testedusing SDL ATLAS Pneumatic Bursting tester (Model 229P)with a specimen of 30mm in diameter according to ISO-139388-1 test method

4 Results and Discussion

41 Analysis of Model Performance The graphical operationof the fuzzy prediction model has been depicted with anexample in Figure 8 For simple expression only one fuzzyrule out of twenty four has been shown in the picture Asper this rule if knitting stitch length (SL) is low (L) yarncount (YC) is low (L) and yarn tenacity (YT) is medium(M) then output fabric bursting strength (BS) will be Level

Figure 8 Rule viewer

SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3

Figure 9 Surface plot showing the impact of stitch length and yarncount on bursting strength

5 (L5) For example if input SL is 28mm YC is 28Ne andYT is 155 gtex then fuzzy expert model predicted outputBS is 330 kPa Using MATLAB Fuzzy Toolbox the fuzzycontrol surface was developed as shown in Figures 9 and 10These can serve as a visual depiction of how the fuzzy expertsystem operates dynamically over time The images show therelationship between knitting stitch length (SL) yarn count(YC) and yarn tenacity (YT) on the input side and burstingstrength (BS) on the output side The surface plots shown inFigures 9 and 10 depict the impact of stitch length yarn countand yarn tenacity on bursting strength

42 Analysis of Experimental Results Effects of stitch lengthyarn count and yarn tenacity on bursting strength have beenshown in Figures 11 and 12 It is obvious from Figure 11 thatdecrease in knitting stitch length from 30mm to 27mmonlyslightly increases the fabric bursting strength Approximatelybursting strength increases 15ndash20 with a decrease of 10in stitch length The reason for an increase in burstingstrength with a decrease in stitch length is probably dueto increasing number of loops per unit area which bears


153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS

Figure 10 Surface plot showing the impact of stitch length and yarntenacity on bursting strength

27 28 29 30Stitch length (mm)

YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)

Figure 11 Effect of stitch length and yarn count on burstingstrength


YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)

Figure 12 Effect of stitch length and yarn tenacity on burstingstrength

the multidirectional forces On the other hand the effect ofdecreasing the stitch length is not linear as a consequencewhile the stitch length decreases further than an optimal levelproduced fabric turns more stiffer and less extensible henceresulting in fabric holes as well as poor bursting strength

A similar phenomenon has been observed for yarn counton bursting strength as shown in Figure 11 It shows that fabricbursting strength increases a little with the decrease of yarncount and vice versaThe bursting strength increases 30ndash40with a decrease of 30 in yarn count due to the increasing ofyarn linear density which would result in increase in burstingstrength Since effect of yarn count on bursting strength is notlinear as a result produced fabric turns much stiffer and lessextensible while the yarn count decreases with a lower stitchlength more than an optimal point and hence leads to poorbursting strength

In contrast the effect of yarn tenacity on the burstingstrength is much more reflective as compared to stitchlength as shown in Figure 12 The figure shows that fabricbursting strength increases drastically with the increase inyarn tenacity and vice versa The bursting strength increasesby about 40ndash50 with the increase of 3 in yarn tenacityBasically yarn is the main material for fabrics and yarntenacity indicates the yarn strength thus when yarn tenacityincreases fabric strength increases However it was foundfrom Figure 12 that knitting stitch length and yarn tenacityhave strong effect on fabric bursting strength The exten-sibility of the fabric decreases whilst the yarn tenacity isincreased further at lower stitch length levels and as a resultthe bursting strength exhibits a descending tendency

From this investigation it is clearly observed that yarntenacity has the greatest and main effect on bursting strengthas compared to knitting stitch length and yarn count There-fore it is very important to maintain optimum level ofknitting parameter in the knitting process in order to achievethe required bursting strength with good quality fabrics

43 Validation of Fuzzy Prediction Model The developedfuzzy prediction model has been validated by experimentaldata Prediction was done using the fuzzy logic rule viewerThe results from the developed fuzzy model were thencompared with 12 validated experimental results as shown inTable 4The correlations between predicted values and exper-imental values of fabric bursting strength are also representedin Figure 13 The coefficient of determination (1198772) betweenthe experimental bursting strength and that predicted bythe fuzzy model was found to be 0961 Therefore it can beconcluded that the developed fuzzy model can explain up to961 of the total variability of fabric bursting strength Themean absolute error (MAE) between the actual values and thepredicted values of bursting strength was found to be 26(lt 5) The absolute error gives the deviation between thepredicted and experimental values and it is required to reachtowards zero The results of the coefficient of determination(1198772) and mean absolute error (MAE) indicate that thedeveloped fuzzymodel has very strong prediction ability witha great accuracy


Table 4 Comparison of predicted and experimental values of fabric bursting strength

Number Stitch length(mm)

Yarn count(Ne)

Yarn tenacity(gtex)

Predictedbursting strength

Experimentalbursting strength

Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099

Mean absolute error () 260Coefficient of determination (1198772) 0961

310 350 390 430 470270Experimental values of BS (kPa)

270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613

Figure 13 Correlation between experimental and fuzzy modelpredicted values of bursting strength

5 Conclusions

In this research investigation fuzzy model has been devel-oped for predicting the fabric mechanical properties likebursting strength of viscoselycra plain knitted fabric Theprediction model was made by taking the knitting stitchlength yarn count and yarn tenacity as input variables andfabric bursting strength as output variable The developedprediction model confers an excellent understanding aboutthe interaction between knitting process variables and theireffects on the fabric bursting strength From the experimentalstudy it has been found that yarn tenacity has the greatest andmain effects on the fabric bursting strength than that of yarncount and knitting stitch length The fuzzy model derived inthis research has been verified from the experiment data

The mean absolute error (MAE) and coefficient of deter-mination (1198772) between the experimental bursting strengthand that predicted by the fuzzy model were found to be 26

and 0961 respectivelyThe results exhibit an excellent predic-tion performance of the developed fuzzymodel Hence it canbe decisively concluded that the developed fuzzy model canbe applied in the textile industry as a decisionmaking supporttool for the production engineer to predict the mechanicalproperties of viscose knitted fabrics satisfactorily

Competing Interests

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

Acknowledgments

The authors are thankful to the management of textileresearch laboratory of APS and APS Textile APS GroupBangladesh for providing the facilities for this research work

References

[1] H Jamshaid T Hussain and Z A Malik ldquoComparison ofregression and adaptive neuro-fuzzy models for predicting thebursting strength of plain knitted fabricsrdquo Fibers and Polymersvol 14 no 7 pp 1203ndash1207 2013

[2] I Hossain A Hossain and I A Choudhury ldquoColor strengthmodeling of viscoseLycra blended fabrics using a fuzzy logicapproachrdquo Journal of Engineered Fibers and Fabrics vol 10 no 1pp 158ndash168 2015

[3] I Hossain A Hossain I A Choudhury A Bakar and HUddin ldquoPrediction of fabric properties of viscose blendedknitted fabrics by fuzzy logic methodologyrdquo in Proceedings ofthe International Conference onMechanical and Civil and Archi-tectural Engineering 2014 (ICMCAE rsquo14) (IISRO rsquo14) pp 100ndash106 Kuala Lumpur Malaysia February 2014

[4] S Mavruz and R T Ogulata ldquoTaguchi approach for theoptimisation of the bursting strength of knitted fabricsrdquo FIBERSamp TEXTILES in Eastern Europe vol 79 no 2 pp 78ndash83 2010


[5] T Shaikh S Chaudhari and A Varma ldquoViscose rayon alegendary development in the man made textilerdquo InternationalJournal of Engineering Research and Application vol 2 no 5 pp675ndash680 2012

[6] S Ertugrul and N Ucar ldquoPredicting bursting strength ofcotton plain knitted fabrics using intelligent techniquesrdquo TextileResearch Journal vol 70 no 10 pp 845ndash851 2000

[7] P GUnalM E Ureyen andDMecit ldquoPredicting properties ofsingle jersey fabrics using regression and artificial neural net-workmodelsrdquo Fibers and Polymers vol 13 no 1 pp 87ndash95 2012

[8] M C Bahadir S K Bahadir and F Kalaoglu ldquoAn artificial neu-ral networkmodel for prediction of bursting strength of knittedfabricsrdquo in Proceedings of the International Conference onMachine Learning and Computer Science (IMLCS rsquo12) pp 167ndash170 August 2012

[9] A Majumdar and A Ghosh ldquoYarn strenghth modeling usingfuzzy expert systemrdquo Journal of Engineered Fibers and Fabricsvol 3 no 4 pp 61ndash68 2008

[10] P Hatua A Majumdar and A Das ldquoModeling ultraviolet pro-tection factor of polyester-cotton blended woven fabrics usingsoft computing approachesrdquo Journal of Engineered Fibers andFabrics vol 9 no 3 pp 99ndash106 2014

[11] M Zeydan ldquoModelling the woven fabric strength using artifi-cial neural network and Taguchi methodologiesrdquo InternationalJournal of Clothing Science and Technology vol 20 no 2 pp104ndash118 2008

[12] E Haghighat S S Najar and S M Etrati ldquoThe prediction ofneedle penetration force inwovendenim fabrics using soft com-puting modelsrdquo Journal of Engineered Fibers and Fabrics vol9 no 4 pp 45ndash55 2014

[13] L A Zadeh ldquoFuzzy setsrdquo Information and Computation vol 8pp 338ndash353 1965

[14] KM U Darain M Z Jumaat M A Hossain et al ldquoAutomatedserviceability prediction of NSM strengthened structure usinga fuzzy logic expert systemrdquo Expert Systems with Applicationsvol 42 no 1 pp 376ndash389 2015

[15] M Gopal Digital Control and State Variable Methods Con-ventional and Intelligent Control Systems Tata McGraw-HillEducation Pvt Ltd Singapore 3rd edition 2009

[16] M Verma and K K Shukla ldquoApplication of fuzzy optimizationto the orienteering problemrdquo Advances in Fuzzy Systems vol2015 Article ID 569248 12 pages 2015

[17] M Vadood ldquoPredicting the color index of acrylic fiber usingfuzzy-genetic approachrdquoThe Journal of the Textile Institute vol105 no 7 pp 779ndash788 2014

[18] C-C Huang andW-H Yu ldquoControl of dye concentration pHand temperature in dyeing processesrdquo Textile Research Journalvol 69 no 12 pp 914ndash918 1999

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



Basically strength of fabrics depends on starting fabricforming materials such as yarn properties and fabric densityThe literature review revealed that various studies have beenreported on the factors affecting the bursting strength ofknitted fabric including yarn type yarn count yarn tenacityyarn breaking elongation yarn breaking strength yarn twistyarn evenness fabrics GSM fabric wale and courses knittingstitch length cover factor tightness factors and relaxationtreatment [1 4 6ndash8]

Moreover all these factors affecting the bursting strengthof knitted fabrics are nonlinear and interactive with otherHence it poses a great challenge for scientists and engineersto develop effectively an exact model based on mathematicaland statistical techniques [2 9] This is ascribed to the factthat both mathematical and statistical models often fail tocapture the nonlinear relationship between inputs and out-puts [10]

On the other hand the intelligent systems such asartificial neural network (ANN) and adaptive neuroinferencesystem (ANFIS) models which have the ability to model innonlinear domain have been applied by few researchers inthe previous research for predicting the bursting strengthof knitted fabrics Jamshaid et al applied ANFIS model topredict the bursting strength of plain knitted fabrics as afunction of yarn tenacity knitting stitch length and fabricGSM [1] Ertugrul and Ucar applied intelligent techniquenamely ANN and ANFIS models for the prediction ofbursting strength of the knitted fabrics using yarn strengthyarn elongation and fabric GSM as input variables [6] Unalet al presented ANN model for the prediction of burstingstrength as a function of yarn strength yarn count yarnevenness yarn twist yarn elongation and fabric wales andcourses [7] Bahadir et al used ANNmodel for the predictionof bursting strength of knitted fabrics [8] Zeydan studiedANN model for the prediction of woven fabric strength [11]However ANN and ANFIS models need large amounts ofnoisy input-output data for model parameters optimizationwhich are challenging labor intensive and time consumingprocesses to collect from the textile knitting industries [1 29] In addition ANN does not tell the core logic based onwhich decisions can be taken [10]

In this regard fuzzy expert system (FES) is found to bethe scientific and engineering solution for quality modelingas FES provides reliable prediction outcome with smallexperimental data in nonlinear and ill-defined textile domain[2 9] Moreover a fuzzy model is more reasonable cheaperin design cost and much easier to apply in comparisonto other models Furthermore fuzzy logic is used to solveproblems in which descriptions of behavior and observationsare imprecise vague and uncertain [2 9 10]

The key purpose of this work is to construct fuzzy intel-ligent model for predicting the bursting strength of viscoselycra plain knitted fabrics as a function of knitting stitchlength yarn count and yarn tenacity which is not reportedin the published literature

2 Materials and Method

21 Fuzzy Expert System The artificial intelligence fuzzyexpert system is a structure of multivalued logic and an

Fuzzifier

Crisp input Rule based

Inference engine

Crisp output

Defuzzifier

Figure 1 Fundamental unit of a fuzzy expert system [2 15]

extension of crisp logic derived from fuzzy mathematical settheory developed by Zadeh in 1965 [9 12 13] In crisp logicsuch as binary logic variables are true or false black or whiteand 1 or 0 If the set under investigation is 119860 testing of anelement 119909 using the characteristics function 119909 is expressed asfollows

120583119860 (119909) =

1 if 119909 isin 119860

0 if 119909 notin 119860(1)

A fundamental fuzzy logic unit comprises a fuzzifier a fuzzyrule base an inference engine and a defuzzifier as shown inFigure 1 [2 14 15]

Fuzzifier Fuzzifier is the first block in the fuzzymodeling thatconverts all numeric inputs-outputs into fuzzy sets withina range from 0 to 1 such as low medium and high byusingmembership functions [12]There are different forms ofmembership function such as triangle trapezoid and Gaus-sian [16] Amongnumerousmembership functions the trian-gular shaped membership function is the simplest and mostfrequently applied which is defined as follows [2]

120583119860 (119909 119886 119887 119888) =

119909 minus 119886

119887 minus 119886 119886 le 119909 le 119887

119888 minus 119909

119888 minus 119887 119887 le 119909 le 119888

0 otherwise

(2)

In this case the edge of the variablersquos interval may berepresented with linear S-shaped and Z-shaped membershipfunctions described respectively as follows

(i) S-shaped membership functions are

120583S (119909 119886 119887) =

1 119909 le 119886

119887 minus 119909

119887 minus 119886 119886 le 119909 le 119887

0 119909 ge 119887

(3)

(ii) Z-shaped membership functions are

120583Z (119909 119886 119887) =

0 119909 le 119886

119909 minus 119886

119887 minus 119886 119886 le 119909 le 119887

1 119909 ge 119887

(4)










120572119894= 120583119860119894(SL) and 120583119861119894 (YC) and 120583119862119894 (YT)

119894 = 1 2 119899

(5)

120583119862 (BS) =

119899

⋃

119894=1

[120572119894and 120583119862119894(BS)] (6)







119911 =sum119899

119894=1120583119894(119887119894)

sum119899

119894=1120583119894

(7)


119894



MAE = 1

N

119894=119873

sum

119894=1

(

10038161003816100381610038161003816119864a minus 119864p

10038161003816100381610038161003816

119864atimes 100)

1198772= 1 minus (

sum119894=119873

119894=1(119864a minus 119864p)

2

sum119894=119873

119894=1(119864a minus 119864M)

2)

(8)














Defuzzification

Aggregation







SL (1198941) =

1198941 27 le 119894

1le 30

0 otherwise

YC (1198942) =

1198942 24 le 119894

2le 36

0 otherwise

YT (1198943) =

1198943 1525 le 119894

3le 1575

0 otherwise

BS (1199001) =

1199001 270 le 119900

1le 460

0 otherwise

(9)

where 1198941 1198942 and 119894







VL HL M


0

05

1


VL HL M


0

05

1





HL M


0

05

1


L1 L2 L3 L4 L5 L6 L7 L8 L9 L10


0

05

1











120583119871 (SL) =

1198941minus 27

28 minus 27 27 le 119894

1le 28

29 minus 1198941

29 minus 28 28 le 119894

1le 29

0 1198941ge 29

(10a)

120583119871 (SL) =

0

27+005

275+1


005

285+0

29 (10b)

120583119871 (YC) =

1198942minus 24

28 minus 24 24 le 119894

2le 28

32 minus 1198942

32 minus 28 28 le 119894

2le 32

0 1198942ge 32

(11a)

120583119871 (YC) =

0

24+05

26+1


05

30+0

32 (11b)

120583119872 (YT) =

1198943minus 1525

155 minus 1525 1525 le 119894

3le 155

1575 minus 1198943

1575 minus 155 155 le 119894

3le 1575

0 1198943ge 1575

(12a)

120583119872 (YT)

= 0

1525+004

1535+

1


06

1565+

0

1575

(12b)


12057210= min (120583

119871 (SL) 120583119871 (YC) 120583119872 (YT))

= min (1 1 1) = 1(13)


12058310 (BS) = min 1 120583

1198715 (BS) (14)














SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3





153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












120572119894= 120583119860119894(SL) and 120583119861119894 (YC) and 120583119862119894 (YT)

119894 = 1 2 119899

(5)

120583119862 (BS) =

119899

⋃

119894=1

[120572119894and 120583119862119894(BS)] (6)







119911 =sum119899

119894=1120583119894(119887119894)

sum119899

119894=1120583119894

(7)


119894



MAE = 1

N

119894=119873

sum

119894=1

(

10038161003816100381610038161003816119864a minus 119864p

10038161003816100381610038161003816

119864atimes 100)

1198772= 1 minus (

sum119894=119873

119894=1(119864a minus 119864p)

2

sum119894=119873

119894=1(119864a minus 119864M)

2)

(8)














Defuzzification

Aggregation







SL (1198941) =

1198941 27 le 119894

1le 30

0 otherwise

YC (1198942) =

1198942 24 le 119894

2le 36

0 otherwise

YT (1198943) =

1198943 1525 le 119894

3le 1575

0 otherwise

BS (1199001) =

1199001 270 le 119900

1le 460

0 otherwise

(9)

where 1198941 1198942 and 119894







VL HL M


0

05

1


VL HL M


0

05

1





HL M


0

05

1


L1 L2 L3 L4 L5 L6 L7 L8 L9 L10


0

05

1











120583119871 (SL) =

1198941minus 27

28 minus 27 27 le 119894

1le 28

29 minus 1198941

29 minus 28 28 le 119894

1le 29

0 1198941ge 29

(10a)

120583119871 (SL) =

0

27+005

275+1


005

285+0

29 (10b)

120583119871 (YC) =

1198942minus 24

28 minus 24 24 le 119894

2le 28

32 minus 1198942

32 minus 28 28 le 119894

2le 32

0 1198942ge 32

(11a)

120583119871 (YC) =

0

24+05

26+1


05

30+0

32 (11b)

120583119872 (YT) =

1198943minus 1525

155 minus 1525 1525 le 119894

3le 155

1575 minus 1198943

1575 minus 155 155 le 119894

3le 1575

0 1198943ge 1575

(12a)

120583119872 (YT)

= 0

1525+004

1535+

1


06

1565+

0

1575

(12b)


12057210= min (120583

119871 (SL) 120583119871 (YC) 120583119872 (YT))

= min (1 1 1) = 1(13)


12058310 (BS) = min 1 120583

1198715 (BS) (14)














SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3





153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












Defuzzification

Aggregation







SL (1198941) =

1198941 27 le 119894

1le 30

0 otherwise

YC (1198942) =

1198942 24 le 119894

2le 36

0 otherwise

YT (1198943) =

1198943 1525 le 119894

3le 1575

0 otherwise

BS (1199001) =

1199001 270 le 119900

1le 460

0 otherwise

(9)

where 1198941 1198942 and 119894







VL HL M


0

05

1


VL HL M


0

05

1





HL M


0

05

1


L1 L2 L3 L4 L5 L6 L7 L8 L9 L10


0

05

1











120583119871 (SL) =

1198941minus 27

28 minus 27 27 le 119894

1le 28

29 minus 1198941

29 minus 28 28 le 119894

1le 29

0 1198941ge 29

(10a)

120583119871 (SL) =

0

27+005

275+1


005

285+0

29 (10b)

120583119871 (YC) =

1198942minus 24

28 minus 24 24 le 119894

2le 28

32 minus 1198942

32 minus 28 28 le 119894

2le 32

0 1198942ge 32

(11a)

120583119871 (YC) =

0

24+05

26+1


05

30+0

32 (11b)

120583119872 (YT) =

1198943minus 1525

155 minus 1525 1525 le 119894

3le 155

1575 minus 1198943

1575 minus 155 155 le 119894

3le 1575

0 1198943ge 1575

(12a)

120583119872 (YT)

= 0

1525+004

1535+

1


06

1565+

0

1575

(12b)


12057210= min (120583

119871 (SL) 120583119871 (YC) 120583119872 (YT))

= min (1 1 1) = 1(13)


12058310 (BS) = min 1 120583

1198715 (BS) (14)














SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3





153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




HL M


0

05

1


L1 L2 L3 L4 L5 L6 L7 L8 L9 L10


0

05

1











120583119871 (SL) =

1198941minus 27

28 minus 27 27 le 119894

1le 28

29 minus 1198941

29 minus 28 28 le 119894

1le 29

0 1198941ge 29

(10a)

120583119871 (SL) =

0

27+005

275+1


005

285+0

29 (10b)

120583119871 (YC) =

1198942minus 24

28 minus 24 24 le 119894

2le 28

32 minus 1198942

32 minus 28 28 le 119894

2le 32

0 1198942ge 32

(11a)

120583119871 (YC) =

0

24+05

26+1


05

30+0

32 (11b)

120583119872 (YT) =

1198943minus 1525

155 minus 1525 1525 le 119894

3le 155

1575 minus 1198943

1575 minus 155 155 le 119894

3le 1575

0 1198943ge 1575

(12a)

120583119872 (YT)

= 0

1525+004

1535+

1


06

1565+

0

1575

(12b)


12057210= min (120583

119871 (SL) 120583119871 (YC) 120583119872 (YT))

= min (1 1 1) = 1(13)


12058310 (BS) = min 1 120583

1198715 (BS) (14)














SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3





153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in













SL

300

350

400

BS

35

YC30

2527 275 28 285 29 295

3





153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




153154

155156

157

YT 2728 285 29 295

3

275 SL

300320340360380400

BS



YC 24YC 30YC 34

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)



YT 1525YT 155YT 1575

250

300

350

400

450

500

Burs

ting

stren

gth

(kPa

)










Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Yarn count(Ne)

Yarn tenacity(gtex)



Absolute error()

1 27 34 1525 310 308 0652 28 34 1525 290 290 0003 29 34 1525 310 324 4324 3 34 1525 278 267 4125 27 30 155 350 351 0286 28 30 155 330 342 3517 29 30 155 350 329 6388 3 30 155 324 310 4529 27 24 1575 452 468 34210 28 24 1575 410 403 17411 29 24 1575 452 458 13112 3 24 1575 410 406 099



270

310

350

390

430

470

Pred

icte

d va

lues

of B

S (k

Pa)

R2= 09613


5 Conclusions




Competing Interests


Acknowledgments


References



























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article predicting the mechanical properties of...

Documents