Determination of Quality Value of Cotton Fiber Using Integrated Best-Worst Method-Revised Analytic Hierarchy Process

ABSTRACT

Selection of cotton fibers in terms of their quality value has created a domain of emerging interest among the researchers. In this study, a newly developed Best-Worst Method (BWM) was integrated with Revised Analytic Hierarchy Process (RAHP) to rank cotton fiber lots on the basis of six apposite fiber properties namely fiber bundle tenacity, elongation, micronaire, upper half mean length, uniformity index, and short fiber index. Ranking performance of this integrated approach closely resembles those of the other multi-criteria decision-making (MCDM) approaches. No occurrence of rank reversal during the sensitivity analyses corroborates the stability and robustness of the BWM-RAHP method. Uniqueness of the present study lies in the fact that this is the maiden application of the vector-based BWM approach, that uses fewer pairwise comparisons than other variants of MCDM, in a cotton fiber grading problem. The RAHP adds value to the decision model by overcoming the problem of ranking inconsistency. Rank correlations between the ranking based on quality value of cotton and those based on yarn tenacity are also encouraging, and further bolster the efficacy of the BWM-RAHP method.

摘要

从质量价值的角度选择棉花纤维，在研究人员中产生了一个新的兴趣领域. 在本研究中，将新开发的最佳-最差方法（BWM）与修订的层次分析法（RAHP）相结合，根据六种适当的纤维特性，即纤维束韧度、伸长率、马克隆值、上半平均长度、均匀度指数和短纤维含量，对棉纤维批次进行排名. 这种综合方法的排名性能与其他多准则决策方法非常相似. 灵敏度分析过程中没有出现秩反转，这证实了BWM-RAHP方法的稳定性和稳健性. 本研究的独特性在于，这是基于向量的BWM方法在棉花纤维分级问题中的首次应用，该方法比MCDM的其他变体使用更少的成对比较. RAHP通过克服排名不一致的问题为决策模型增加了价值. 基于棉花质量值的排名与基于纱线韧度的排名之间的排名相关性也令人鼓舞，并进一步增强了BWM-RAHP方法的有效性.

KEYWORDS:

• AHP
• BWM
• cotton
• MCDM
• quality value
• sensitivity analysis

关键词:

• 棉
• 质量价值
• 敏感性分析

Introduction

Cotton being a natural cellulosic fiber possesses widely varying physical characteristics. The majority of these physical properties have a vital influence (up to 80%) in controlling the quality of the final yarn (USTER News Bulletin 1991). Cotton fiber properties such as tenacity, elongation, uniformity index, length (upper half mean length), fineness, and short fiber content exert a great influence on spun yarn properties and processing performance like end breakage rate (Majumdar, Sarkar, and Majumdar 2004). But the level of influence is diverse and varies depending upon the yarn manufacturing technologies/systems, i.e., ring, rotor or air jet spinning system. For example, contribution of fiber length to yarn tenacity is 22% and 12% for ring and rotor spinning technologies, respectively (USTER News Bulletin 1991). This is due to the fact that very long fibers may act as a wrapper or belt in case of rotor spinning and thus they fail to contribute toward yarn tenacity. Therefore, determination of the technological value or quality value of cotton fiber has become an appealing domain of textile research. The existing methods or tools like Fiber Quality Index (FQI), Spinning Consistency Index (SCI), Premium-Discount Index (PDI) which are used frequently in cotton spinning industries to determine the technological value of cotton fibers (Kang et al. 2000; Mogazhy and Gowayed 1995a, 1995b) are not so efficient in handling the cotton fiber selection problem. For example, FQI and SCI do not provide a very good correlation between the cotton fiber ranking and the real-ranking of yarn properties (Majumdar, Majumdar, and Sarkar 2005). PDI, although, provides the highest rank correlation between the fiber quality and yarn property, requires past data to create a regression model which cannot be done for any new samples without any past data (Majumdar, Majumdar, and Sarkar 2005; Majumdar, Sarkar, and Majumdar 2005). To overcome the shortcomings of the above three existing methods, several researchers over the years have considered the cotton grading and selection issues as the decision-making problems and addressed the said issues using various exponents of Multi-Criteria Decision Making (MCDM) technique. MCDM is a branch of Operations Research (OR) and management science, and is used to select the best alternative or to rank a set of alternatives considering multiple (often conflicting) criteria.

Majumdar, Sarkar, and Majumdar (2004) employed Analytic Hierarchy Process (AHP) of MCDM to grade 8 cotton fiber lots using six fiber properties. Majumdar, Majumdar, and Sarkar (2005) compared the performance of AHP with FQI, SCI and PDI. In a subsequent study, Majumdar, Sarkar, and Majumdar (2005) applied a hybrid approach consisting of AHP, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to rank 33 cotton fiber lots by determining their quality values. To address the inherent vagueness or imprecision involved during pair-wise comparison, Majumdar (2010) deployed Fuzzy-AHP method in cotton fiber selection problem, and reported better performance of the said method than the conventional models. Majumdar and Singh (2014) demonstrated a new approach by integrating TOPSIS with the genetic algorithm (GA). TOPSIS was used to determine the comprehensive quality value of cotton fibers, whereas GA was used to optimize the weights of the fiber attributes. Chakraborty, Das, and Kumar (2017) proposed Grey Fuzzy Logic approach comprising Grey Relational Analysis (GRA) and Fuzzy Logic (FL) for solving a cotton fiber selection problem. Chatterjee and Chakraborty (2018) proposed an integrated approach consisting of Design of Experiment (DoE) and TOPSIS for the determination of technological value of cotton fibers taking into consideration six apposite cotton fiber properties.

The MCDM techniques have also been used for various other textile applications like grading of raw jute fibers (Ghosh and Das 2013; Das and Ghosh 2021), selection of hand-made carpets (Gupta 2022), selection of cotton fabrics (Jing and Chen 2021, 2022; Mitra et al. 2015), and designing of textile products (Akgül et al. 2021) to mention a few. Ghosh and Das 2013 proposed a hybrid method integrating AHP and TOPSIS for grading of 10 jute lots considering fiber strength, defect, root content, color, fineness, and bulk density as the six decision criteria. Later Das and Ghosh (2021) extended the work and demonstrated a fuzzy multi-criteria group decision-making method for grading of jute fibers. Jing and Chen (2021) proposed Pythagorean Fuzzy-TOPSIS approach for selecting the best cotton fabric from a competitive lot based on several properties affecting fabric comfort. In another research work, Jing and Chen (2022) proposed an integrated approach comprising of Pythagorean fuzzy sets (PFSs) and the Preference Ranking Organization Method for Enrichment of Evaluation (PROMETHEE) for the selection of cotton fabric considering fuzziness and uncertainty involved in the process. Akgül et al. (2021) proposed a TOPSIS based MCDM method for designing different linen-based textile products in coloration through madder, a natural source. Gupta (2022) demonstrated a comparative study using three MCDM methods, namely Weighted Sum Model (WSM), Weighted Product Model (WPM), and TOPSIS for the selection of handmade carpets by evaluating their overall durability using four decision criteria, namely abrasion loss, compression recovery, loss of thickness after dynamic loading, and loss of thickness after prolonged heavy static loading.

From the ongoing discussion, it is noted that researchers, over the years, deployed MCDM techniques in various textile applications including cotton fiber grading and selection. However, no study has been done till date to demonstrate the applicability of the newly developed Best-Worst Method (BWM) in the textile domain in general, and in cotton fiber grading problem in particular.

To fill this gap, this paper demonstrates, for the first time, an integrated approach using newly developed BWM and a modified version of RAHP to solve cotton grading problem based on quality value. The efficacy of the present approach is judged by various sensitivity analyses.

Research methodology

Multi-criteria decision making –– an overview

Multi-Criteria Decision Making (MCDM) is a decision support system tool and includes various methods or approaches which are broadly classified into two groups: Multi-Objective Decision Making (MODM) which addresses decision problems having continuous decision space, and Multi-Attribute Decision Making (MADM) involving discrete decision variables which are predetermined and finite in number. Goal programming, Goal attainment, etc., fall under the first category. On the contrary, AHP, TOPSIS, COPRAS (COmplex PRoportional ASsessment), PROMETHEE, EDAS (Evaluation based on Distance from Average Solution), MOORA (Multi-Objective Optimization on the basis of Ratio Analysis) are some of the widely used variants of MADM (Chen 2016, 2020; Ghorabaee et al. 2016, 2017; Hwang and Yoon 1981; Mitra 2020, 2021).

Best-Worst Method (BWM)

The vector-based BWM was proposed by Rezaei, Wang, and Tavasszy (2015) as a new MADM method which compares the best (i.e., most desirable or most important) criterion to the other criteria and all other criteria to the worst (i.e., least desirable or least important) criterion. The main objective of this method is to determine the optimal weights of the criteria and the consistency ratio through a structured comparison system utilizing a simple linear optimization technique (Ahmadi, Kusi-Sarpong and Rezaei 2017; Ghaffari et al. 2017; Rezaei 2015a, 2015b; Rezaei et al. 2016).

Backdrop of the development of Best-Worst Method (BWM)

Pairwise comparisons which is the backbone of any hierarchical decision-making method, usually suffer from the problem of inconsistency. The handling of inconsistency problem poses a major challenge to the decision makers (DMs). The main underlying cause being the unstructured way of making comparison during pairwise comparison (Rezaei 2015a). BWM is one of the novel MCDM methods which is preferred over other exponents such as AHP because of the following key advantages:

• If n is the number of attributes, then BWM requires only (2n − 3) number of comparisons whereas AHP requires n$\times$(n − 1)/2 comparisons.

• Both integers and fractional numbers must be used, in general, when using a comparison matrix. In AHP, for example, both integers 1, 2 …9, and fractional numbers ½, ⅓ … ⅛ need to be used (Table 1). In BWM, on the contrary, only integers are used, which makes it more convenient for the DMs.

Table 1. The 9-Point fundamental relational scale proposed by T.L. Saaty (1980).

Intensity of importance	Definition	Explanation
1	Equal importance	Two activities contribute equally to the objective.
3	Moderate importance	Experience and judgment slightly favor one activity over another.
5	Essential or strong importance	Experience and judgment strongly favor one activity over another.
7	Very strong importance	An activity is very strongly favored and its dominance is demonstrated in practice.
9	Extreme importance	The evidence favoring one activity over another is of the highest possible order of affirmation.
2, 4, 6, 8	Intermediate values between two adjacent judgments	When compromise is needed.
Reciprocals	If activity p has one of the above numbers assigned to it when compared with activity q, then q has the reciprocal value when compared with p.

Various steps of Best-Worst Method (BWM)

The various steps involved in BWM to derive optimal weights of criteria on the basis of reference comparisons only are summarized below:

Step 1: To determine the set of decision criteria

The set of decision criteria $\left\{c_1,c_2,\cdots ,c_n\right\}$ for the present problem is determined, in this step.

Step 2: To determine the best and the worst criteria

The DM identifies the best (i.e., most desirable or most important) and the worst (i.e., least desirable or least important) criteria in general without making any comparison at this stage.

Step 3: To determine the preference of the best criterion over all other criteria

In this step, the preference of the best criterion over all other criteria (i.e., the Best-to-Others vector) is determined using a scale 1 through 9, which can be expressed as follows:

$A_B=\left(a_{B1},a_{B2},a_{B3},\cdots ,a_{Bn}\right)$

Here, $a_{Bj}$ is the preference of the best criterion B over criterion j. So, $a_{BB}=1$.

Step 4: To determine the preference of all other criteria over the worst criterion

The preference of all other criteria over the worst criterion (i.e., the Others-to-Worst vector) is determined using a scale 1 through 9 as before. The resultant vector can be expressed as:

$A_W={\left(a_{1W},a_{2W},a_{3W},\cdots ,a_{nW}\right)}^T$

Here, $a_{jW}$ denotes the preference of criterion j over the worst criterion W. Here, $a_{WW}=1$.

Step 5: To determine the optimal weights of the criteria $\left(W_1^{\ast },W_2^{\ast },W_3^{\ast },\cdots ,W_n^{\ast }\right)$

The optimal weight of each criterion $W_j^{\ast }$ is the one where $\frac{W_B}{W_j}=a_{Bj}$ and $\frac{W_j}{W_W}=a_{jW}$. In order to satisfy this, we have to find a solution so that the maximum absolute differences $\left|\frac{W_B}{W_j}-a_{Bj}\right|$ and $\left|\frac{W_j}{W_W}-a_{jW}\right|$ are minimized for all j. The following problem results when we consider the non-negativity and sum condition for the weights:

$minma{x}_j\left\{\left|\frac{W_B}{W_j}-a_{Bj}\right|,\left|\frac{W_j}{W_W}-a_{jW}\right|\right\}$

such that

(1) $\sum _j{W}_j=1,\mathrm{a}\mathrm{n}\mathrm{d}{W}_j\ge 0\mathrm{\forall }j$(1)

The above model can be transformed to the following linear model:

$min\xi$ such that

$\left|\frac{W_B}{W_j}-a_{Bj}\right|\le \xi$ and $\left|\frac{W_j}{W_W}-a_{jW}\right|\le \xi$

(2) $\sum _j{W}_j=1,\mathrm{a}\mathrm{n}\mathrm{d}{W}_j\ge 0\mathrm{\forall }j$(2)

Solving the model (2), we get optimal weights $\left(W_1^{\ast },W_2^{\ast },W_3^{\ast },\cdots ,W_n^{\ast }\right)$ and ${\xi }^{\ast }$ (Liang, Brunelli, and Rezaei 2020; Rezaei 2015a).

Step 6: Consistency checking in BWM

Rezaei (2015a) proposed an output-based consistency ratio (CR) as shown in Equation (3)(3) $CR=\frac{{\xi }^{\ast }}{CI}$(3) , using the optimal objective value, ${\xi }^{\ast }$, and the corresponding consistency index (CI) as a measure to check the consistency of BWM. CI, in this case, refers to the maximum possible values of $\xi$, which are 0.00, 0.44, 1.00, 1.63, 2.30, 3.00, 3.73, 4.47, 5.23 for n = 1–9, respectively (Ali and Rashid 2021; Rezaei 2015a).

(3) $CR=\frac{{\xi }^{\ast }}{CI}$(3)

The values of CR may lie within the range [0, 1]. The closer the value of CR is to 0 the more consistent the judgments of the DM are. The judgment becomes cardinally consistent when CR = 0 (Liang, Brunelli, and Rezaei 2020).

Analytic Hierarchy Process (AHP) and Revised Analytic Hierarchy Process (RAHP)

AHP, the most prevalent approaches of MCDM, can handle both the tangible and intangible attributes, and possesses the capability to elicit the weights of criteria and scores of alternatives through the formation of pair-wise comparison matrices. Based on the principle of hierarchical comparisons, it is a powerful and practical tool of decision-making in which the best alternative can be expressed (for the maximization case) by the Equation (4)(4) $A_{AHP}=max{\sum }_{j=1}^n{S}_{ij}.W_{j}fori=1,2,3,\dots ,m$(4) :

(4) $A_{AHP}=max{\sum }_{j=1}^n{S}_{ij}.W_{j}fori=1,2,3,\dots ,m$(4)

where, n is the number of criteria, m is the number of alternatives, S_ij is the relative performance score of the i-th alternative with respect to j-th criterion, such that $\sum _{i=1}^m{S}_{ij}=1$, and W_j is the relative weight of j-th criterion.

Details of AHP can be found in published literatures (Mitra et al. 2015; Mitra 2022; Saaty 1980, 1983, 1986, 1990). The AHP family of methods ranges from absolute, distributive, ideal, and supermatrix modes for scaling weights in the process of ranking alternatives (Millet and Saaty 2000; Saaty 1994; Saaty and Vargas 1993). Most of these variants suffer from rank reversal problem or inconsistencies (Majumdar et al. 2021). To overcome this, Belton and Gear (1983) proposed an ideal mode of AHP, also known as RAHP, in which the dataset is normalized using Equation (5)(5) $N_{ij}=\frac{S_{ij}}{Max\left(S_{ij}\right)},\left(forbenefitattribute\right)$(5) and Equation (6)(6) $N_{ij}=\frac{Min(S_{ij})}{S_{ij}},\left(forcostattribute\right)$(6) depending upon the nature of attributes:

(5) $N_{ij}=\frac{S_{ij}}{Max\left(S_{ij}\right)},\left(forbenefitattribute\right)$(5)

and

(6) $N_{ij}=\frac{Min(S_{ij})}{S_{ij}},\left(forcostattribute\right)$(6)

where S_ij is the score of i-th alternative with respect to j-th attribute, and N_ij is the corresponding normalized score.

The flowchart of the hybrid BWM-RAHP method is given in Figure 1.

Figure 1. Flowchart of BWM-RAHP hybrid method.

Experimental

The dataset for this study comprises the fiber testing results of 17 cotton lots and corresponding ring-spun yarn data for three different yarn counts (16 Ne, 22 Ne, and 30 Ne). All the yarns were spun using same twist multiplier (TM) so that effect of twist is nullified. Table 2 shows the minimum, maximum, average and standard deviation of considered fiber parameters. Six cotton fiber properties, namely fiber bundle tenacity (FS), elongation (FE), upper half mean length (UHML), uniformity index (UI), micronaire value (FF), and short fiber index (SFI), which possess very strong influence on various yarn properties, are taken as the six decision criteria. This is to be noted that the micronaire value of cotton fiber is an indicator of fiber fineness and maturity. The micronaire value is determined by measuring the air flow through a compressed cotton plug. In other words, cotton micronaire is determined by measuring the resistance to airflow of a cotton fiber plug with specified mass compressed to a fixed volume. It is unitless. All the tests have been carried out using High Volume Instrument (HVI) which is used in most of the cotton spinning industries. The instrument is calibrated except for the elongation using standard cotton samples.

Table 2. Summary statistics of cotton fiber properties.

Cotton fiber properties	Minimum	Maximum	Mean	Standard deviation
Fibre bundle tenacity (cN/tex)	26.5	30.8	28.78	1.07
Fibre elongation (%)	5.3	6.7	6.24	0.45
Upper half mean length (inch)	0.97	1.15	1.06	0.05
Uniformity index	79.2	83.2	81.47	1.11
Short fiber index (%)	6.8	15.1	9.9	2.10
Fibre micronaire	3.1	4.7	4.09	0.43

The main analysis is divided into two parts: 1) Determination of optimal weights of the six fiber criteria using the BWM and 2) Determination of quality value of cotton and ranking using RAHP method.

Results and discussion

Determination of weights of cotton fiber properties

For determination of the quality value of the cotton fibers, six properties namely FS, FE, FF, UHML, UI, and SFI are identified as the set of decision criteria, here. Among the six criteria, UHML is assumed to be the best (i.e., most important) criterion, and FE is assumed to be the worst (i.e., least important) criterion. The pairwise comparisons of the Best-to-Others and those of the Others-to-Worst criteria are shown in Table 3.

Table 3. Pairwise comparison for best-to-others criteria and others-to-worst criteria.

Comparison	FS	FE	FF	UHML	UI	SFI
Best criterion (UHML) to others	1	7	3	1	2	2
Other criterion to the Worst criterion (FE)	7	1	2	7	4	4

Considering the data furnished in Table 3, the following linear optimization model (Equation 7(7) $\sum _j{W}_j=1,\mathrm{a}\mathrm{n}\mathrm{d}{W}_j\ge 0\mathrm{\forall }j$(7) ) is developed to find out the optimal weights of the criteria and the optimal objective/output value of the present problem:

(7) $\sum _j{W}_j=1,\mathrm{a}\mathrm{n}\mathrm{d}{W}_j\ge 0\mathrm{\forall }j$(7)

Here, $W_{FS}^{\ast },W_{FE}^{\ast },W_{FF}^{\ast },W_{UHML}^{\ast },W_{UI}^{\ast },and{W}_{SFI}^{\ast }$ are the optimal weights of the six criteria mentioned above, respectively. Solving the linear model, we get:

$W_{FS}^{\ast }=0.284,W_{FE}^{\ast }=0.039,W_{FF}^{\ast }=0.091,W_{UHML}^{\ast }=0.289,W_{UI}^{\ast }=0.148,$

$W_{SFI}^{\ast }=0.148,and{\xi }^{\ast }=0.011$. Hence, the optimal weights of FS, FE, FF, UHML, UI, and SFI are found to be 0.284, 0.039, 0.091, 0.289, 0.148, and 0.148, respectively.

Measurement of consistency ratio

Since, preference of the best to the worst criterion, i.e., $a_{BW}=7$, in this case, the consistency index (CI) for this problem is chosen as 3.73 from Table 4. This gives: CR = ${\xi }^{\ast }/CI$ = 0.011/3.73 = 0.0029, which implies a very good consistency.

Table 4. Consistency Index (CI) values of BWM (Rezaei 2015a).

$a_{BW}$	1	2	3	4	5	6	7	8	9
CI (max $\xi$)	0.00	0.44	1.00	1.63	2.30	3.00	3.73	4.47	5.23

Ranking of cotton fibers based on quality value

Once criteria weights are determined using BWM, the next phase is to apply the RAHP method to rank the available cotton fibers based on their quality values. Initially, the decision matrix is normalized using Equations (5)(5) $N_{ij}=\frac{S_{ij}}{Max\left(S_{ij}\right)},\left(forbenefitattribute\right)$(5) and (6(6) $N_{ij}=\frac{Min(S_{ij})}{S_{ij}},\left(forcostattribute\right)$(6) ) depending upon the nature of criteria, i.e., whether they are benefit (higher-the-better type) or cost (lower-the-better type). The final priorities, i.e., quality values of cotton fibers are determined using Equation (4)(4) $A_{AHP}=max{\sum }_{j=1}^n{S}_{ij}.W_{j}fori=1,2,3,\dots ,m$(4) . The normalized values of six fiber parameters, quality values of cotton fibers determined by the proposed BWM-Revised AHP method, and yarn tenacity corresponding to different yarn count are presented in Table 5 which shows that fiber lot F9 achieves rank 1 (the best) whereas lot F7 occupies rank 17 (the worst) in terms of quality value. These results comply with the earlier findings reported by researchers (Banwet and Majumdar 2014; Chakraborty, Das, and Kumar 2017; Majumdar and Singh 2014).

Table 5. Results based on BWM-RAHP analysis and yarn tenacity.

Cotton fiber lots	Results of BWM-RAHP approach								Results based on yarn tenacity
	Normalized scores						Quality value	Ranking	16 Ne		22 Ne		30 Ne
	FS	FE	FF	UHML	UI	SFI			Tenacity	Ranking	Tenacity	Ranking	Tenacity	Ranking
F1	0.932	0.970	0.705	0.948	0.974	0.615	0.878	12	15.30	6	14.47	7	13.52	11
F2	0.925	0.985	0.886	1.000	0.964	0.713	0.921	5	14.77	12	13.78	14	13.64	8
F3	0.932	0.851	0.838	0.957	0.952	0.456	0.861	14	13.98	17	13.15	17	12.28	17
F4	1.000	0.955	0.721	0.983	0.993	0.901	0.953	2	16.24	3	15.21	2	14.88	1
F5	0.860	0.866	0.816	0.948	0.980	1.000	0.921	4	14.49	14	14.42	8	13.11	14
F6	0.893	0.940	0.689	0.930	0.995	1.000	0.919	6	14.60	13	14.77	5	14.06	4
F7	0.948	0.791	0.689	0.852	0.962	0.506	0.828	17	15.15	10	13.24	16	13.47	12
F8	0.942	1.000	0.738	0.913	0.984	0.778	0.900	8	15.19	9	14.01	12	13.77	7
F9	0.984	1.000	0.705	0.957	1.000	0.981	0.954	1	16.28	2	14.75	6	14.41	3
F10	0.912	0.940	0.816	0.878	0.970	0.556	0.851	16	14.15	16	13.35	15	13.10	15
F11	0.994	0.985	0.660	0.930	0.999	0.947	0.939	3	16.39	1	15.26	1	14.86	2
F12	0.932	1.000	0.795	0.913	0.974	0.750	0.897	10	14.38	15	13.96	13	13.08	16
F13	0.919	0.970	0.816	0.843	0.980	0.643	0.859	15	15.45	5	15.10	3	13.97	5
F14	0.942	0.985	1.000	0.922	0.970	0.745	0.919	7	15.62	4	14.27	10	13.55	10
F15	0.899	0.821	0.660	0.913	0.980	0.733	0.867	13	15.25	8	14.18	11	13.82	6
F16	0.945	0.910	0.775	0.913	0.982	0.764	0.898	9	14.99	11	14.93	4	13.63	9
F17	0.929	0.851	0.738	0.904	0.990	0.752	0.885	11	15.26	7	14.28	9	13.22	13

*Here, yarn tenacity in cN/tex.

Validation of the results

A 4-phase sensitivity analysis was performed to demonstrate the robustness of the BWM-RAHP hybrid approach. The 1^st phase includes comparison of the present approach with the earlier approaches. The 2^nd phase investigates the efficacy of the proposed approach by changing the weightage level of the decision criteria. The 3^rd phase demonstrates sensitivity analysis in dynamic decision conditions, and the 4^th phase draws comparison between ranking based on quality value using the present approach and that based on yarn tenacity.

Comparison with earlier approaches

Table 6 shows the comparative ranking performances of different approaches performed on the same cotton fiber selection problem. The comparison is done on the basis of Spearman’s Rank Correlation analysis expressed mathematically by Equation 8.(8) $R_s=1-\frac{6{\sum }_{i=1}^m{D}_i^2}{m\left(m^2-1\right)}$(8)

(8) $R_s=1-\frac{6{\sum }_{i=1}^m{D}_i^2}{m\left(m^2-1\right)}$(8)

Table 6. Comparison of ranking performance between different methods.

Method	BWM-RAHP	Grey Relational Grade (GRG)	Grey Fuzzy Logic (GFRG)	TOPSIS-GA	AHP-TOPSIS	GA-TOPSIS
BWM-RAHP	-	0.9289	0.9207	0.8211	0.8922	0.6103
Grey Relational Grade (GRG)	-	-	0.9764	0.8309	0.8922	0.6961
Grey Fuzzy Logic (GFRG)	-	-	-	0.8557	0.9035	0.7387
TOPSIS-GA	-	-	-	-	0.9534	0.9191
AHP-TOPSIS	-	-	-	-	-	0.8186

where D_i denotes the absolute difference between two rankings, and m denotes the total number of alternatives which is 17, in this case. It is found that in majority of the cases, there are very high correlations (>0.8) between the ranking obtained from the BWM-RAHP method and those of earlier approaches, indicating good agreement in their ranking patterns.

Sensitivity analysis through changing the weightage of criteria

A sensitivity analysis is performed in this phase through increasing and decreasing the weights of each of the six decision criteria in six steps. Here, the weight of the target criterion is changed by±10%, ±20%, and±30%, in steps, with respect to the nominal value, and adjusting the weights of remaining criteria proportionately in such a way that $\sum _{j=1}^n{w}_j=1and{w}_j\ge 0,j\in \left\{1,2,3,\dots ,n\right\}.$ Ranking is then done using RAHP method taking the new weight combinations, in each phase (Mitra 2021). For each target criterion, six new ranking patterns are obtained (corresponding to weightage level −10%, −20%, −30%, +10%, +20%, and+30% with respect to the nominal weight of the target criterion). So, considering six target criteria, 36 new ranking patterns are generated, in total. The rank correlations between the newly generated ranking sets and the nominal (original) ranking pattern are shown in Table 7 which reveals that the rank correlations are 1 or very close to 1 in most of the cases, the minimum coefficient being 0.975. It implies that there is hardly any change in ranking order (or occurrence of rank reversal) due to the change in criteria weight up to±30%. So, it can be emphasized that the ranking elicited by the hybrid BWM-RAHP method is robust enough even when the weightage of the criteria is changed significantly in either (i.e., positive or negative) direction.

Table 7. Correlations of rankings at different levels of weights of target criterion.

Target criteria	Change in weightage level of target criterion w.r.t. nominal weight
	−30%	−20%	−10%	+10%	+20%	+30%
FF	0.993	0.993	0.998	0.998	0.980	0.980
SFI	0.983	0.985	0.985	0.995	0.988	0.988
FS	0.998	0.998	0.998	0.988	0.978	0.975
FE	1	1	1	1	0.998	0.995
UHML	0.975	0.988	0.988	0.998	0.995	0.995
UI	0.998	0.998	0.998	1	0.998	0.998

Sensitivity analysis with different number of cotton fibers

A few scenarios are simulated in this phase by altering the number of alternatives in the original decision matrix. The new scenarios are simulated in the following way: from the current decision matrix, the worst alternative is eliminated for the subsequent consideration. In each scenario, BWM-RAHP method is applied to rank the remaining alternatives considering those as the elements of the newly simulated decision matrix, keeping all other parameters unchanged. As per the initial ranking of cotton fibers, the alternatives can be arranged as: F9 > F4 > F11 > F5 > F2 > F6 > F14 > F8 > F16 > F12 > F17 > F1 > F15 > F3 > F13 > F10 > F7. From this original solution, F7 is discarded in the first simulated scenario (SN-1), since it is the worst alternative. So, in SN-1, a new simulated decision matrix with 16 cotton lots is generated, on which BWM-RAHP method is deployed again to get a new ranking pattern. After SN-1, the order of 16 cotton lots are: F9 > F4 > F11 > F5 > F2 > F6 > F14 > F8 > F16 > F12 > F17 > F1 > F15 > F3 > F13 > F10. Cotton lot F9 remains the best choice while F10 becomes the worst in the first scenario (SN-1). Similarly, for the remaining 15 simulated scenarios (from SN-2 through SN-16), the BWM-RAHP method is executed in iterative manner, to get 15 ranking solutions. The overall results of this dynamic analysis depicted in Figure 2 reveal no occurrence of rank reversal, at all. This implies stability and robustness of the BWM-RAHP approach in dynamic decision condition, too.

Figure 2. Performance of BWM-RAHP model during dynamic decision conditions.

Validation by comparing quality value-based ranking with tenacity ranking

At the final stage of validation, the ranking based on quality value using the hybrid BWM-RAHP approach is compared with the ranking based on yarn tenacity for three different yarn counts, and the results are presented in Table 5 and Figure 3. Ranking offered by BWM-RAHP method bears the rank correlation coefficients (R_s) of 0.414, 0.542, and 0.566 with tenacity rankings for 16 Ne, 22 Ne and 30 Ne yarn counts, respectively. These are better than many of the traditional methods, and can be improved further by improving the pairwise comparisons.

Figure 3. Comparison between quality value-based ranking and yarn tenacity ranking.

Conclusion

A hybrid approach integrating newly developed BWM with revised AHP is deployed in this study to rank cotton fibers based on their quality value. Weights of the six fiber criteria are determined by the vector-based BWM method as it is capable of giving a consistent result every time using a fewer number of pairwise comparisons. The optimal weights for the six fiber criteria, i.e., FS, FE, FF, UHML, UI, and SFI are found to be 0.284, 0.039, 0.091, 0.289, 0.148, and 0.148, respectively. The final ranking of 17 fiber lots is done by the RAHP method.

Cotton fiber lot F9 achieves rank 1 (the best) whereas lot F7 occupies rank 17 (the worst) in terms of quality value. This complies with the earlier findings. The overall ranking yielded by the present approach bears a very high correlation with the earlier approaches. The stability and robustness of the present approach are investigated through various sensitivity analyses. During sensitivity analysis through altering weights of criteria, the newly generated rankings are found to be so close to each other that the rank correlations are 1 or almost 1, with the minimum coefficient being 0.975. When sensitivity analysis is performed by discarding the worst alternative in steps, no occurrence of rank reversal is observed at all.

Finally, the quality value-based ranking using BWM-RAHP method is compared with the yarn tenacity-based ranking for three different yarn count levels, i.e., 16 Ne, 22 Ne and 30 Ne. The obtained rank correlation coefficients are encouraging and better than those attained by many of the traditional methods.

However, the weightage of the six cotton fiber properties obtained through BWM depends on the perception of the decision makers. Therefore, by adjusting the scores given in the pair-wise comparison, a suitable weightage for the fiber parameters can be obtained. The main contribution of the paper revolves around the methodology proposed and not the absolute weightage assigned to various fiber parameters. The performance of the present method can be improved further by improving the reference comparisons during BWM approach by incorporating clear understanding about the influence of various cotton fiber criteria on the final yarn properties.

The novelty of the present study lies in the fact that this is a maiden ever attempt using BWM as a weighting method in the domain of textiles. BWM possesses some unique features uncommon in other variants of MCDM. Although it involves fewer pair-wise comparisons (reference comparisons only rather than secondary comparisons), it gives consistent weights of the criteria each time. It involves simple mathematical equations, and is quite flexible having no limitations of the number of criteria and alternatives. BWM together with RAHP forms a robust decision-making model devoid of the problem of rank inconsistency. Application of this newly developed BWM method can be integrated to other MCDM exponents and extended to other domains of textile industry, as well, to solve any real-world decision problem.

The highlights of the present research are as under

• This is a maiden ever application of Best-Worst Method (BWM), as a criteria-weighting tool, in the domain of textiles, in general, and cotton selection problem, in particular.

• The vector-based BWM possesses some unique features uncommon in other variants of MCDM. It gives consistent results (i.e., criteria weights) every time using a fewer number of pair-wise comparisons (on the basis of reference comparisons only) than popularly used AHP method.

• BWM together with Revised AHP (RAHP) forms a robust decision-making model devoid of the problem of rank inconsistency. BWM is used to determine optimal weights of the criteria, whereas RAHP is used for final ranking and selection of cotton fibers based on quality value.

• Ranking performance of this integrated approach closely resembles those of the earlier approaches. No occurrence of rank reversal during the sensitivity analyses corroborates the stability and robustness of the BWM-RAHP method. Moreover, the BWM-RAHP method performs better in real-life situation compared to the traditional methods of cotton grading, as envisaged by better correlations between ranking given by present approach and those based on yarn tenacity.

• The new approach is simple, comprising a few simple mathematical equations, and quite flexible having no limitations of the number of criteria and alternatives.

• Application of this newly developed BWM method can be integrated to other MCDM exponents and extended to other domains of textile industry, as well, to solve any real-world decision problem.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

There is no funding involved in this research/study.