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Applicationof a Multi-Criteria Decision Making Approach to Determine the IdealCombination of Length-Diameter Blended Fiber

Applicationof a Multi-Criteria Decision Making Approach to Determine the IdealCombination of Length-Diameter Blended Fiber

1.Introduction

Severalstudies have been conducted to assess the application of MCDM totextile. An algorithm developed by Majumbar et al. [1] works bycombining genetic algorithm and TOPSIS to determine the overallquality of cotton fiber. The algorithm uses two properties of a yarn,which include unevenness and tenacity. Majumbar et al [2] also usedTOPSIS and AHP to develop software that is used to select and gradecotton fiber. In addition, the AHP model has been advanced and it cannow be used to facilitate the selection of raw materials that areused in the textile industry [3]. Moghassem and Bahramzadeh [4]assessed the possibility of applying the TOPSIS model to obtain theoptimum spinning conditions of a yarn used in weft knitting machine.The final ranking indicated that a doffing tube that had no torquestopped while the setting was found to have a coefficient that wascloser to an ideal solution. The suitable components of the doffingtube and its alteration for rotor spun were picked by an extendedTOPSIS model.

Moghassemand Fallahpor [5] used the TOPSIS approach to select the suitablesetting in the spinning machine for the Ne 30 rotor yarn used in weftknitting fabric. The TOPSIS approach was proposed as an alternativemodel for detection of yarn and control system [6]. Additionally, theselection of the rotor spinning machine that determines the qualityparameters of the yarn can be investigated using a combination of AHPand TOPSIS approaches [7]. AHP alone can be used to assess therelative significance of the overall quality of the yarn. The finalranking navels were drawn out in line with the relative closeness ofa value that was determined using the TOPSIS approach. The ELECTREoutranking approach can be used to choose the rotor navel asindicated by Kaplan, Araz, and Goktepe [8]. Mitra *etal.*[9] developed an index handloom fabric quality that was applied inthe selection of fabrics for certain end use.

TheMAHP and AHP multi-criteria decision making (MCDM) models wereapplied in the ranking of about 25 handloom cotton fibers. The cottonfabric was ranked in terms of its quality, bearing in mind itsapplicability as a clothing material for summer. Hao *etal.*[10] tested the liberation of different stitch-bonded fabrics withdifferent hemp content under various conditions of temperature,moisture, humidity, transmissibility, and water retention. Multipleproperties of quick drying and moisture absorption indicated that thetested performance of the five factors was applied in developing theevaluation system while TOPSIS approach was used to build a morecomprehensive evaluation model. Duru and Candan [11] used acombination of AHP and TOPSIS to choose the most appropriatealternative for drying and wicking features of the seamless garment.Hong and Su [12] applied the combination of TOPSIS and Taguchiapproaches to establish the optimal processing criteria for PET/TiOUV-resistant cotton fiber melt-spinning, which was accomplished usinga minimum number of scientific experiments.

Dulange*etal.*[13] established the success factors that influence the overallperformance of power loom textiles. The researcher evaluated theeffect of these factors on performance of the organization, with theobjective of identifying their impact on performance of medium sizedfirms in solar industrial sector. This was accomplished using the AHPmodel. Yicel and Guneri [14] established a model that sets off theweakness and complete the fuzzy multi-objective linear method for theselection of suppliers. Yaylaet al. [15] employed the TOPSIS model to choose the suitable supplierof garment X in Turkey. Eleren and Yilmaz [16], on the other hand,employed TOPSIS to develop a model that could be used to choosesuppliers in the textile industry in Usak. Tanyas [17] developed asystem that could be used to perform evaluation in the global textilesourcing office. The system relied on the balanced scorecard approachwith the aid of the AHP method within the perspective of the supplychain.

2.3.Optimization of TOPSIS approach and Analytic Hierarchy Process (AHP)

Theprocess of making decision involves the selection of alternativesthat are considered to be more feasible out of all available options.The multi-criteria process of making decisions includes one level ofengineering and one level of management. TOPSIS model is an exampleof multi-criteria method that is used to find solutions from thefinite set of the available options [2]. AHP is a flexible andpowerful multi-criteria tool for decision making that is employed tostructure a complicated process of making decisions in differentlevels. Both the quantitative and qualitative aspects of decisionmaking are considered [19]. A combination of AHP and TOPSIS makes itpossible to choose the ideal fiber length-diameter that adds value toanimal fibers and enhance the quality of yarns. In the case of anAHP-TOPSIS hybrid, a pair-wise comparison approach of AHP is mergedwith the rest of TOPSIS steps. The procedure of AHP-TOPSIS hybrid isexpressed in a set of steps [22-22], as shown below

Step1:The step involves the identification of the relevant goals.

Step2:Involves the formulation of alternatives and criteria for decisionmatrix using the information that is already available. Letter Mrepresents the number of options or alternatives, while N stands forthe number of criteria. Elements a_{ij}and_{}D_{mxn}standfor the actual value of i^{th}optionin terms of jth^{}adecision matrix.^{}

Step3:Involves the conversion of the decision matrix to a normmalizedmatrix with normalixed value r_{ij}being computed as follows

Step4:The relative significance of various criteria, with respect to thegoals of underlying problem is determined using the AHP model. Ascale of relative significance is used to construct a pair-wisecomparison matrix. The fundamental scale of the model of AHP is usedto enter the judgements as shown in Table 2 and Table 3. In the caseof N criteria, the size of comparison matrix is NxN and cij denotesthe significance of criteria i with respect to j. The element c_{ij}=1when i=j and. The pair-wise matrix of criteria should be as shownbelow. The importance and normalized weight of i^{th}criteria (Wi) should be determined by computing the geometric averageof i^{th}row (GMi) of the matrix. The geometric average of rows is thennormalized as follows Consistency ration (CR) and consistency indexare computed using the equation below, where λmax represents themaximum value of eigen and RCI stands for the random consistencyindex where its value can be found in Table 4. The judgment isconsidered to be consistent and acceptable when the value of CR is0.1 or less. The decision maker needs to reconsider the entries ofthe pair-wise matrix in case the CR value is more than 0.1.

Step5:The weighted and normalized value of υ_{ij}should be computed as shown below, where *W*_{i}stands for the weight of the*i*_{th}attribute.

Step6:The negative and positive ideal solutions are determined using theformula shown below where i is related to the benefit criteria whileJ is related to the cost criteria.

Step7:In this step, the separation measure, which is determined usingn-dimensional Euclidean distance, should be computed.

Step8:In this step, the relative closeness to an ideal solution iscomputed.

Where*d*−*j*≥0 and *d*+*j*≥0 and Rj∈[0, 1]

Step9:At this stage, all options are arranged in a descending order withrespect to the value of R_{j}.

3.Results and discussion

*Amulti-criteria decision method *

Thetenacity, unevenness, thin as well as thick places, hairiness, neps,ends-down, and elongation was taken as weights in order to performthe evaluation of TOPSIS. Analytical hierarchy was employed todetermine the weights of the eight decision criteria. This is done inaccordance with the relative significance of yarn performance asshown in Table 6. A comparison was done on the basis of the Saaty’snine-point scale as shown in Table 3. The score documented in Table 6stand for perception of the decision-maker. However, scores may varyfrom decision maker to another. Codes of the eight criteria andweights are computed as shown in Table 7. Original matrix wasmultiplied by a weight vector in order to determine original matrix’smeasure of consistency. This was achieved with the help of equationshown in step 3, λ_{max,}anddocumented in step 4.

WhereCI=0 and <0. Normalization of the vector was made andnormalization matrix weighted before the negative as well as negativeideal solutions could be computed (Table 8).

Theseparation of each option from the ideal solution was then computedby employing equation 5 and 6, which was done after identifying thenegative (A-) and positive (A+) ideal solutions. The relativecloseness of different options to the ideal solution was thendetermined using equation shown in Step 9 with respect to thepositive ideal solution. The level of closeness of the coefficientvalue to the ideal solution, which is abbreviated as Rj,was used to rank the preference order of all options. This was donein a descending order as illustrated in Table 9.