Sustainable supplier selection under attractive criteria through FIS and integrated fuzzy MCDM techniques

ABSTRACT

Suppliers as upstream partners play a crucial role to establish sustainability in the supply chain. For precise evaluation of the supplier’s performance on sustainability criteria researchers have mainly focused on Multi-Criteria Decision Making (MCDM) and Fuzzy Inference System (FIS) approaches. The objective of the paper is to evaluate the supplier’s sustainability performance through FIS and fuzzy MCDM approaches. Further, the results are compared and utilised to develop the Sustainable Supplier Selection (SSS) framework for the iron and steel industry of India. To calculate Suppliers Performance Index (SPI), three distinct FIS engines have been developed for each sustainability dimensions and fuzzy AHP and TOPSIS techniques are used for the MCDM environment. The results provide a deep inside of the sustainability performance of each supplier. It elicits from the results of two approaches, that ranks are interchanged among the top two suppliers.

KEYWORDS:

• Sustainability
• sustainable supplier selection
• Fuzzy Inference System (FIS)
• fuzzy AHP
• Fuzzy TOPSIS
• fuzzy MCDM

1. Introduction

Ever-increasing judicial pressure and increasing stakeholder’s awareness about the environment and social rights have forced industries to take up initiatives to achieve sustainability objectives in their supply chain and manufacturing processes (Ahmadi et al. 2017; Jafarian 2013; Luthra, Garg, and Haleem 2015; Luthra et al. 2017). On the other hand, industries are also aware of the various benefits of sustainability attainment and have initiated the incorporation of social and environmental aspects along with economic traits (Tavana, Yazdani, and Di Caprio 2016; Azadnia et al. 2013). However, for effective integration of sustainability dimensions into supply chains, the industry needs to acquire the support and cooperation of all upstream and downstream supply chain partners (Amindoust et al. 2012; Roy et al. 2019). Suppliers are upstream partners and can contribute significantly to the attainment of the sustainability objectives in the industry (Büyüközkan and Gizem 2011; Luthra et al. 2017; Ghadimi, Dargi, and Heavey 2017; KhanMohammadi et al. 2018). Hence the sustainable supplier selection is a strategic decision for the industry (Kumar and Rahman 2015; Tavana, Yazdani, and Di Caprio 2016; Orji and Wei 2015; Ghadimi et al. 2019).

The conventional Supplier Selection (SS) process was based on economic criteria and supplier’s performance on social and environmental criteria was not considered. However, Sustainable Supplier Selection (SSS) requires supplier’s performance evaluation on economic, social and environmental dimensions i.e. Triple Bottom Line (TBL) guidelines (Shalke et al. 2018; Chaharsooghi and Ashrafi 2014; Zimmer, Fröhling, and Schultmann 2016; Vinodh, Mulanjur, and Thiagarajan 2013; Yazdani, Chatterjee, and Torkayesh 2020). But the consideration of economic, environmental and social dimensions in a single decision frame made decision-makers handle a large number of criteria. The handling of such a large number of sustainability criteria is a major challenge and the possible solution is criteria clustering (Jain and Singh 2019). Therefore for accomplishing the SSS process, DM’s require to develop clusters of evaluation criteria in three sustainability dimensions.

Saxena et al. (2017) defined clustering as unsupervised learning where the objects are grouped on the basis of some similarity inherent among them. Criteria analysis encompasses various algorithms and methods for grouping objects of a similar kind into respective categories such that the degree of association between two objects in the same group is maximum and minimal otherwise. Authors have developed various criteria clustering methods such as K- means algorithm, Artificial Neural Network, self-organising Maps, etc. (Terlunen, Barreto, and Hellingrath 2015).

Jain and Singh (2019) have considered sixty-six sustainability criteria significant for SSS in a large scale industry. Authors have applied the fuzzy Kano model for clustering the sustainability criteria into four main clusters, Must be, One dimensional, Attractive, and Indifferent. Further, the authors have applied the Type IV Kano model for three subclassifications of Must be and Attractive cluster criteria.

Sustainable supplier assessment framework in the industry requires human reasoning based input. These inputs have inherited imprecision and vagueness (Azadnia et al. 2013; Singh, Olugu, and Fallahpour 2014). Hence to cope with the vagueness, the proposed decision framework focuses on the application of FIS for SSS for a large scale industry incorporating Attractive criteria. Application of FIS provides more precise and accurate results as it incorporates the knowledge of industry experts in establishing the fuzzy rules set which enables precise evaluation of suppliers. Hence DMs need to take optimum decisions concerning the desired accuracy and the number of rules. Some researchers have used FIS for addressing the issue of SSS (Amindoust and Saghafinia 2016; Ghadimi, Dargi, and Heavey 2017; Pourjavad and Shahin 2018). However, the authors have not performed the criteria clustering in their models.

In literature, various researchers and academicians have also proposed Multi-Criteria Decision Making (MCDM) based techniques for SSS as MCDM techniques are well suited for structuring complex problems (Mardani et al. 2015; Igarashi, De Boer, and Fet 2013; Ho, Xiaowei, and Dey 2010; Chai, Liu, and Ngai 2013; Govindan et al. 2015; Agarwal et al. 2011). However, to perform the evaluation of potential suppliers, response from DM’s in linguistic terms are required. But linguistic response lacks the subjectivity as decision-makers express their qualitative perceptions in the quantitative form (Amindoust et al. 2012; Liu et al. 2019) To address this issue authors have integrated fuzzy logic concepts with MCDM techniques for addressing the SSS process (Ho, Xiaowei, and Dey 2010; Mardani et al. 2015). However, fuzzy logic integrated MCDM techniques fall short in the handling of a large number of sustainability criteria. The number of mathematical calculations increases in fuzzy MCDM as the number of alternatives are increased. Hence in the proposed decision framework, the fuzzy MCDM technique has been applied considering criteria clustering. However, fuzzy logic-based MCDM techniques fall short in the handling of a large number of sustainability criteria and complex & larger mathematical calculations are involved when the number of alternatives is more. Therefore to overcome these restrictions and to capture the inborn vagueness in DM’s responses, in this work a Fuzzy Inference System (FIS) has been applied. Also in the case of a sustainable supplier selection problem the input parameters need to be critically examined which can be efficiently handled by the FIS system. Further FIS system possess superiority over other fuzzy MCDM techniques (Pourjavad and Shahin 2018; Amindoust et al. 2012) because FIS make use of Rule Base Architecture (RBA) which is more capable of capturing the input parameter through membership function and rule base of FIS.

It is elicited from the literature review that fuzzy AHP and fuzzy TOPSIS are the preferred MCDM techniques (Zimmer, Fröhling, and Schultmann 2016). Hence, in this work, fuzzy analytic hierarchy process (FAHP) has been applied for weight assignment and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) method has been used for supplier assessment and the establishment of Supplier Performance Index (SPI).

The proposed decision framework employs the same decision maker’s team to evaluate the potential suppliers on the same criteria and sub-criteria through two different approaches i.e FIS and FMCDM. SPI obtained from both the approaches are compared and a decision framework has been developed for performing the final selection of a sustainable supplier.

Our research thus contributes to the literature on sustainable supplier selection in the following ways. First, in this work, three distinct FIS engines in each sustainability dimension have been developed for which Attractive criteria and their quantified sub-criteria acts as an input. Second, the proposed methodology considers the values of SPI from FIS and fuzzy MCDM approaches on a single platform and provides robust results to decision-makers to able them to make efficient decisions. Third, in the proposed methodology, the least number of FIS rules need to be framed by DM’s in each FIS engine.

The novelty of the proposed work is its ability to incorporate the crux of MCDM as well as FIS approaches for the final selection of the suppliers. Further, the proposed work incorporates the modified structure of the FIS system which facilitates the DMs to frame the least number of rules for each FIS engine in three sustainability dimensions. The results of the present work provide a better understanding of the supplier’s performance in each sustainability dimension. Further, the results of the two approaches enable the DMs to have a comparative validation through the supplier’s evaluation. It elicits from the results that the supplier’s excelling in one dimension is not performing well in other sustainability dimensions. Hence the overall results convey the overall sustainability performance which helps the DMs to make the final selection.

Another novelty of the proposed work is, in present times when all suppliers are equipped with modern production technology and fulfill the basic criteria of selection the proposed work evaluates supplier’s sustainability on Attractive criteria for final selection. The proposed methodology has been applied to the Indian iron and steel industry as a case company.

The remainder of the paper is organised as follows. In section 2, a literature review on SSS criteria and SSS frameworks with integrated fuzzy set theory along with the research gaps is presented. Section 3 presents the proposed methodology. Section 4 presents the application of the proposed model in the case company and also covers the results of the application of the model. Discussions on the results of the work have been covered in section 5. The managerial implications of the work are discussed in section 6. Finally, a few remarks along with directions for future work have been concluded in section 7.

2. Literature review

In 1966, Dickson carried out the Pioneer research in the field of supplier selection criteria and reported quality, delivery as the criteria of extreme importance and price and technical capability as considerable importance criteria for the supplier selection process. Since Dickson’s work, many authors have reported and advocated the incorporation of new supplier selection criteria due to the emergence of new technologies and also due to the globalisation of markets. Further, due to growing awareness among customers and pressure from government agencies and stakeholders, the incorporation of environmental and social criteria has been done in the supplier selection process (Hussain and Al-Aomar 2018). It is elicited from the Literature review that quantum of work has been done in the field of supplier selection by various researchers. Academicians and researchers have proposed various decision frameworks incorporating different methodologies. It is also elicited from studies on traditional and sustainable supplier selection process, that there are two main issues in supplier selection process, at first establishment of appropriate sustainable criteria for selection and secondly development of a decision framework for evaluation of supplier performance based on criteria and awarding of ranks to suppliers (Govindan, Khodaverdi, and Jafarian 2013). Hence in this section, a brief literature review has been presented on two domains which are critical for the success of SSS.

2.1. Sustainable supplier selection criteria

The selection of efficient suppliers has been a major challenge for the procurement department of industries (Weber 1991) and researchers have addressed the problem of supplier selection comprehensively. Authors have proposed different supplier selection methodologies/frameworks as a possible solution to this problem (Ware, Singh, and Banwet 2012; Ho, Xiaowei, and Dey 2010; Khurrum and Bhutta 2003).

Traditionally the proposed methodologies incorporated only the economic dimension and the majority of the proposed methodology is based on the economic criteria reported by Dickson (1966). Supplier selection was purely based on the supplier’s performance on the economic criteria (Kar and Pani 2014; Wilson 1994; Cheraghalipour and Farsad 2018). However, with the increasing environmental awareness among the customers, environmental criteria were incorporated along with the economic criteria in the supplier selection process (Humphreys, Wong, and Chan 2003; Govindan et al. 2015). Hence due to the inclusion of environmental criteria (Green criteria), SCM was more commonly termed as Green supply chain management (GSCM) (Kuo, Wang, and Tien 2010; Bai and Sarkis 2010; Noci 1997; Igarashi, De Boer, and Fet 2013; Banaeian et al. 2016). In the year 1987 Brundtland commission in its report emphasised the conservation of environment along with development and hence insisted on sustainable development. The report defined sustainable development as ‘development that meets the needs of the present without compromising the ability of future generations to meet their own needs.’ (Bruntland 1987). Thus with the widespread significance of social awareness among various stakeholders, economic, environmental and social criteria were considered simultaneously for supplier selection. Incorporation of all three domains leads to the development of Sustainable Supply Chain Management (SSCM). Among the various objectives of SSCM is the objective of sustainable supplier selection (Rao, Goh, and Zheng 2017). Academicians have addressed the topic and have proposed various MCDM tools based methodologies for supporting and structuring the decision framework (Zimmer, Fröhling, and Schultmann 2016; Nielsen et al. 2014). However, due to different social trends and traits among various cultures in the world, consideration of social characteristics of sustainability in supplier selection is more challenging as a comparison to economic and environmental aspects (Ghadimi, Dargi, and Heavey 2017; Winter and Lasch 2016).

In today’s global market, the industry needs to incorporate sustainability initiatives in its manufacturing process and its supply chains so as to withstand the competition and maintain its current position among the competitors (Cheraghalipour, Paydar, and Keshteli 2018). This makes the establishment of a sustainable supply chain as the prime objective of decision-makers of industries (Hassini, Surti, and Searcy 2012). To address this objective, many methodologies have been proposed by various authors incorporating sustainability criteria for supplier selection in different domains (Luthra et al. 2017; Shaw et al. 2012; Seuring and Muller 2008). However, form the literature it elicits that the authors have not considered the sustainability criteria for selecting the suppliers from the perspective of perceived satisfaction by the industry (Table 1). To attain the highest level of satisfaction from the SSS process sustainability criteria need to be clustered on the basis of criteria priority for the selection process.

Table 1. Sustainable supplier selection methodologies with integrated fuzzy set theory

Author’s	Research objective	Proposed approach	Sustainability dimension	Criteria clustering
Ghadimi, Dargi, and Heavey (2017)	Evaluate and select the most sustainable supplier	Audition checklist and FIS	Economic, social and environmental	Not considered
Mavi, Goh, & Zarbakhshnia, (2017)	Third-party reverse logistic provider evaluation.	Fuzzy SWARA and Fuzzy MOORA	Economic, social and environmental	Not considered
Rao, Goh, and Zheng (2017)	sustainable supplier selection based	Linguistic 2-tuple grey correlation degree.	Economic, social and environmental	Not considered
Fallahpour, Olugu, Musa, Wong, & Noori, (2017)	identify the most sustainable supplier with	Fuzzy AHP and Fuzzy TOPSIS	Economic, social and environmental	Not considered
Singh, Olugu, and Fallahpour (2014)	evaluation of manufacturing sustainability of small and medium enterprises	Fuzzy Inference System	Economic, social and environmental	Not considered
Amir Hossein Azadnia, Zameri, Saman, & Wong, (2015)	Sustainable supplier selection and order allocation combined with multi-period multi-product lot-sizing problem.	Fuzzy AHP and multi-objective mathematical programming	Economic, social and environmental	Not considered
Kannan, (2018)	Sustainable supplier selection	Fuzzy Delphi, ISM, ANP, COPRAS-G	Economic, social and environmental	Not considered
Awasthi et al., (2018)	Globally sustainable supplier selection.	Fuzzy AHP, fuzzy VIKOR,	Economic, social and environmental	Not considered
Pishchulov et al. (2019)	Sustainable supplier selection	Voting Analytic Hierarchy Process (VAHP)	Economic, social and environmental	Not considered
Rashidi and Cullinane (2019)	Sustainable supplier selection	Fuzzy DEA and fuzzy TOPSIS	Economic, social and environmental	Not considered
Khan et al. (2018)	Supplier sustainability performance evaluation and selection	fuzzy-Shannon Entropy and fuzzy- Inference system	Economic, social and environmental	Not considered
Mohammed, Harris, and Govindan (2019)	Sustainable supplier selection and order allocation	Fuzzy AHP and Fuzzy TOPSIS	Economic, social and environmental	Not considered

Kano model is one such criteria clustering method which has been widely adopted by the authors in different research fields such as healthcare, future vehicle driving, online reviews, budget airlines, environmental quality, strategic thinking, student satisfaction, retail service industry, automated vehicles, patient satisfaction, etc. (Min-Yuan, Chen, and Chang 2019; Materla, Cudney, and Antony 2019; Jian-Wu et al. 2019; Wong and Ho 2019; Dace, Stibe, and Timma 2019; Watson 2019; Dinçer, Yüksel, and Pınarbaşı 2020; Stetter 2020; Lucadamo, Camminatiello, and D’Ambra 2020). Kano model has the unique feature of establishing a relationship between DM’s expectations and their satisfaction level. Criteria clustering through the Kano model facilitates DMs to clusters the sustainability criteria on the basis of perceived satisfaction into five main categories.

1. Attractive requirements (A): this cluster includes the requirements that are not expected by the customer in a product, therefore satisfaction level increases on fulfilment, and however nonfulfillment does not bring any dissatisfaction to the customer.

2. Must-be requirements (M): The requirements that are vital and which customer needs to have in the product. The dissatisfaction level significantly increases the Non-fulfilment of these requirements.

3. One-dimensional requirements (O): Customer satisfaction increases if these requirements are met and customer dissatisfaction increases when these requirements are not met. These requirements are performance requirements and are expected by the customer in the product or service offered.

4. In different requirements (I): Customer satisfaction or dissatisfaction is not affected by these requirements.

5. Reverse requirements (R): These requirements are not desired by the customer and the absence of these attributes increases the customer’s satisfaction level.

2.2. Sustainable supplier selection techniques incorporating fuzzy logic

Sustainable supplier selection process’s success depends much on the evaluation of supplier performance with respect to sustainability criteria in linguistic terms (Azadnia et al. 2013; Jain and Singh 2017). Decision-makers respond to supplier evaluation using linguistic terms that are simple and tangible. However, due to the subjective evaluation of qualitative and quantitative criteria, the response of DM’s are encompassing vagueness and uncertainty (Yu et al. 2019). To capture this ambiguity in the response to DM’s, authors have incorporated fuzzy set theory integrated with other decision tools (Jafarian 2013; Amindoust et al. 2012; Orji and Wei 2015).

Fuzzy set theory was developed by Zadeh (1965) for capturing uncertainty and imprecision inherited in human judgement using linguistic terms and degree of membership. Further decision framework in a sustainable environment demands to mesh quantitative and qualitative criteria that traditional approaches fail to achieve (Zimmer, Fröhling, and Schultmann 2016). Thus authors have incorporated fuzzy set theory in their decision frameworks as a natural choice over other approaches. The fuzzy set theory has the capability of dealing with the concepts which are hard to quantify and it also provides crisp outputs for problems having subjectivity (Ghadimi, Dargi, and Heavey 2017). Owing to these benefits, authors have integrated fuzzy set theory with decision tools such as Analytic Hierarchy Process (AHP), Data Envelopment Analysis (DEA), Weighted Aggregated Sum Product Assessment (WASPAS), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), etc. (Zimmer, Fröhling, and Schultmann 2016; Ho, Xiaowei, and Dey 2010; Govindan et al. 2015).

2.3. Research gaps and research objectives formulation

An effective SSS process depends on the identification and establishment of appropriate sustainability criteria (Rashidi and Cullinane 2019; Memari et al. 2019; Giannakis et al. 2020; Naveen Jain and Singh 2020). From the literature review, it is elicited that economic criteria have been mainly focused by authors for establishing the SSS process. Further, few authors have considered environmental criteria along with economic criteria (Bai and Sarkis 2010; Büyüközkan and Gizem 2011; Shen et al. 2013). however, the TripleBottom Line(TBL) approach os sustainability emphasis the consideration of criteria in three i.e social, environmental and economic domains. Hence the first objective of the present work is framed as

Objective 1: Selection of appropriate sustainability criteria cluster in economic, environmental and social dimensions for SSS.

Today, almost all the suppliers have state of the art technology and equipment and hence can provide the industry with quality products at most economical cost. In such a scenario where all suppliers are at par with each other, the industry needs to have a set of criteria that helps to evaluate and distinguish the most potential sustainable suppliers and also to achieve the highest level of satisfaction from the SSS process. Thus the second objective of the work is

Objective 2: Identification of Attractive criteria for better and distinguished supplier evaluation in the SSS process.

The SSS process involves the evaluation of suppliers against a large number of sustainability criteria. Handling such a large number of sustainability criteria is a major challenge for the DMs. Multi-Criteria Decision Making (MCDM) techniques facilitate DMs in choosing the most potential supplier considering several qualitative and quantitative criteria that are often conflicting in nature. However, the MCDM techniques suffer from the drawback that they depend on human judgement pairwise comparison for selection which is biased. Hence, the supplier evaluation needs to be done through the FIS system also, considering the same set of criteria and final selection to be made considering the results of both the approaches.

Objective 3: Development of SSS decision framework with architecture based on MCDM and FIS respectively and considering results of both approaches for final selection.

SSS process encompasses supplier evaluation through human judgement in terms of linguistic responses. As these linguistic terms inherit ambiguity and uncertainty there is a need for capturing the vagueness in the responses. Hence the last objective of the work is framed as

Objective 4: Integrating fuzzy set theory in both MCDM and FIS approaches for capturing the vagueness of DMs in the SSS decision framework.”

3. Proposed methodology

The proposed methodology has been developed for sustainable supplier selection in the iron and steel industry of India. The methodology comprises of six steps as

Step 1: Formation of Decision-makers’ team:

In the initial stage of the methodology, a team of decision-makers is to be formed. The decision-makers should have adequate experience in the industry and should be conversant with the supplier selection process of their organisation. The primary responsibility of the team comprises of formation of a pool potential suppliers from which the final selection can be made.

Step 2: Review of Literature:

A comprehensive literature survey is to be carried out for identification of the industry-specific Sustainable Supplier Selection (SSS) criteria.

Step 3: Sustainability criteria clustering

An efficient SSS framework necessitates the evaluation of suppliers to be performed against a larger number of criteria. However, consideration and handling of a larger number of sustainability criteria present problems for the decision-makers. Hence to facilitate the decision-makers there is a need for clustering of sustainability criteria into meaningful categories based on the priority of criteria form SSS perspective.

Kano model philosophy is a suitable tool for criteria clustering (Jain and Singh 2017). Further, the fuzzification of the Kano model helps in better capturing of the real perception of the DM’s. Application of Fuzzy Kano model, clusters sustainability criteria into four clusters (i) Must be, (ii) One dimensional, (iii) Attractive and (iv) Indifferent cluster. Further, subclassification of the sustainability criteria under the Attractive cluster can be done by using the Type IV Kano model as proposed by Shahin et al. (2013) and applied by Jain and Singh (2019) for clustering of sustainability criteria. Application of Type IV Kano model further subclassify the Attractive cluster into three sub-clusters: Less attractive (A₁), Attractive (A₂) and Highly attractive (A₃).

Step 4: Identification of sub-criteria of the selected cluster

Further, after the subclassification of attractive sustainability criteria, each criterion is individually addressed by DM’s and relevant sub-criteria of attractive sustainability criteria in three dimensions are established for further analysis.

Step 5: Sustainability Performance Index (SPI) calculation through FIS

In this step sub-criteria for three sustainability dimensions are quantified and based on quantified values appropriate range for sub-criteria are established. Further, membership functions are developed which acts as an input for the Fuzzy Inference System (FIS). In this work, the FIS model has been prepared by applying the Mamdani’s compositional rule of inference (Mamdani 1974). Choice of Mamdani FIS over Sugeno inference system is made based on the following points

• It predicts the results reasonably and comprises of a simple structure along with intuitive and interpretable rule base nature (Jassbi et al. 2006).

• In Mamdani FIS a crisp result is obtained by defuzzification of rules’ consequent whereas in Sugeno FIS crisp result is obtained using a weighted average of the rules’ consequent.

• Mamdani FIS is more suitable for human inputs, has expressive power and interpretable rule consequents whereas Sugeno FIS is suitable for mathematical analysis and lacks interpretability.

In this work, three distinct FIS engine has been developed for each sustainability dimension for evaluation of the supplier’s performance on sustainability criteria. The proposed FIS model development consists of three major steps:

3.1. Membership function and operational operators

In this step, DMs consider every sub-criterion and based on their experience and current practices of industry establish the evaluation levels and further quantify these evaluation levels. This quantification provides robustness and reliability to the proposed approach and thus helps in attaining more precise results. However, the evaluation levels established by DMs are subjective and imprecise and hence they need to be converted into the grade of membership. In this FIS model, the membership function for the input variables is developed by considering a triangular form. A triangular form of fuzzy number can be represented as $\tilde{M}$= (a, b, c) as shown in Figure 2 and defined as Eq. (1)(1) ${\mu }_{\tilde{M}}=\left\{\begin{array}{c}0,x<a,\\ \frac{\left(x-a\right)}{\left(b-a\right)},a\le x\le b\\ \frac{\left(c-x\right)}{\left(c-x\right)},b\le x\le c\\ 0,x>c,\end{array}\right\}$(1) .

(1) ${\mu }_{\tilde{M}}=\left\{\begin{array}{c}0,x<a,\\ \frac{\left(x-a\right)}{\left(b-a\right)},a\le x\le b\\ \frac{\left(c-x\right)}{\left(c-x\right)},b\le x\le c\\ 0,x>c,\end{array}\right\}$(1)

In this FIS model, quantified levels of sub-criteria of each sustainability dimension act as input and three fuzzy sets have been applied on these inputs. The linguistic terms used by DMs for evaluating supplier’s performance, assigned to each fuzzy sets are ‘Worst’, ‘Average’ and ‘Best’ as tabulated in Table 2.

Table 2. Linguistic terms for supplier’s evaluation

Linguistic terms	Fuzzy set
Worst	(a, a, b)
Average	(a, b, c)
Best	(b, c, c)

The basic mathematical operations performed on fuzzy numbers are fuzzy addition, fuzzy subtraction, fuzzy division, and fuzzy multiplication. To understand the fuzzy mathematical operations lets us consider two fuzzy numbers as Z1 = (l₁, m₁, u₁) where $l_1\le m_1\le u_1$ and Z2 = (l₂, m₂, u₂), where $l_2\le m_2\le u_2$. The basic mathematical operations considering two fuzzy numbers Z1 and Z2 are represented as shown in Table 3.

Table 3. Fuzzy mathematical operations

Fuzzy mathematical operation	Fuzzy operation	Mathematical evaluation
Fuzzy addition	Z1$\oplus$Z2	(l1 + l2, m1+ m2, u1+ u2)
Fuzzy subtraction	Z1⊝Z2	(l1 – u2, m1- m2, u1- l2)
Fuzzy division	Z1$\oslash$Z2	(l1/u2, m1/m2, u1/l2)
Fuzzy multiplication	Z1⊗Z2	(l1 * l2, m1 * m2, u1 *u2)
Inverse	Z1–1	(l1, m1, u1)-1 ≈ (1/u1, 1/m1, 1/l1)

3.2. Fuzzy rules (KM based) and modified architecture of FIS engine

In this step, the expert’s knowledge is utilised to frame the fuzzy rule sets for the development of the FIS model. The number of fuzzy rules in a FIS model is determined by using Equation (2)(2) $N={\left(M\right)}^V$(2) .

(2) $N={\left(M\right)}^V$(2)

Where

N: represents the number of fuzzy rules

M: represents the number of membership functions and

$V$: represents the number of input variables.

For understanding the utility of Eq (2)(2) $N={\left(M\right)}^V$(2) in determining the number of rules let us consider an example with values of M as 3 and the value of $V$as 2. As per Eq. 2(2) $N={\left(M\right)}^V$(2) , the total number of rules to be framed for FIS are 9. However, if the value of $V$is increased to 3, and keeping the value of M same, then the number of rules to be framed increases to 27 and which further increases to 81 for $V$ = 4. Hence it can be observed from the example that, for the same number of membership functions, the number of rules increases exponentially for a higher number of input variables. As such handling of lager number of rules in FIS is complex and presents a challenge for DMs. Therefore to handle such situations, in the proposed methodology the modified architecture of FIS has applied which facilitates the DMs to handle the least possible number of rules without affecting the accuracy of the results.

3.3. Defuzzification

The fuzzified results of each rule are given as input to the FIS and the output of FIS is used as an input for the defuzzification process for obtaining the results in real numbers. In literature, authors have proposed various types of defuzzification methods such as (i) Centre of Sums Method (COS), (ii) Centre of gravity (COG) or Centroid of Area Method (COA), (iii) Bisector of Area Method (BOA) and (iv) Weighted Average Method. In the proposed FIS, COA method has been used for the defuzzification of the fuzzified results and can be expressed mathematically as Equation (3)(3) $x_{COA}=\frac{{\sum }_{i=1}^n{x}_i{\mu }_i\left(x_i\right)}{{\sum }_{i=1}^n{\mu }_i\left(x_i\right)}$(3)

(3) $x_{COA}=\frac{{\sum }_{i=1}^n{x}_i{\mu }_i\left(x_i\right)}{{\sum }_{i=1}^n{\mu }_i\left(x_i\right)}$(3)

The final output of the defuzzification process is the Performance Index in Economic Dimension (PIED), Performance Index in Social Dimension (PISD), and the Performance Index in Environmental Dimension (PIEND) of each supplier. Further, DM’s assign the weight to each sustainability dimension and based on these three weighted performance indexes the final Sustainability Performance Index (SPI) for each supplier is then calculated as

(4) $SPI={\sum }^{\left\{(W_{economic}\ast PIED)+\left(W_{social}\ast PISD\right)+\left(W_{environmental}\ast PIEND\right)\right\}}$(4)

Where SPI is the Sustainability Performance Index of the supplier evaluated, $W_{economic}$ is the importance weight of PIED, $W_{social}$ is the importance weight of PISD and $W_{environmental}$ is the importance weight of PIEND as decided by the DM’s. The proposed methodology facilitates the decision-makers to decide the weights according to the industry needs and the global scenario. Decision-makers have the liberty to choose different weights by considering any value ranging from 0 to 1. Value 1 represents the highest priority and value 0 signifies no priority to the sustainability dimension.

Step 6: Sustainability Performance Index (SPI) calculation through an integrated fuzzy MCDM method.

In this step, a pairwise comparison of sub-criteria is performed by using the fuzzy AHP technique for the establishment of fuzzy weights of sub-criteria. Further, utilising these fuzzy weights, performance assessment of the suppliers against each sub-criteria is performed by applying the fuzzy TOPSIS method. The performance of each supplier is assessed and Sustainability Performance Index (SPI) for each supplier is determined.

3.4. Fuzzy AHP

AHP is the most preferred MCDM technique for decision modelling (Zimmer, Fröhling, and Schultmann 2016). AHP is a structured decision technique for dealing with complex decision making. Following are the steps of FAHP technique

3.4.1. Establish the pair-wise comparison matrix

Based on the expert opinion the pairwise comparison of factors is being prepared. The experts are required to compare each factor in pairs in a matrix form with size n x n, where n is the number of criteria.

3.4.2. Check for the consistency

To control the consistency of subjective opinions of the decision-makers and to check the accuracy of the weight factors, the consistency factor is calculated as

(5) $CF=\frac{\left({\lambda }_{max}-1\right)}{\left(n-1\right)}$(5)

Where ${\lambda }_{max}$the maximum eigenvalue of the matrix and n is the number of alternatives. If the CF is less than 0.1 then pairwise comparisons are acceptable.

The values of the pairwise comparison matrix are converted into triangular fuzzy numbers

For the construction of fuzzy judgement matrix $\tilde{A}=\left\{{\tilde{a}}_{ij}\right\}$ comprising of n criteria through pairwise comparison using Triangular Fuzzy Numbers (TFN) as

(6) $\tilde{A}=\left[\begin{array}{cccc}1& {\tilde{a}}_{12}& \cdots & {\tilde{a}}_{1n}\\ {\tilde{a}}_{21}& 1& \cdots & {\tilde{a}}_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ {\tilde{a}}_{n1}& {\tilde{a}}_{n2}& \cdots & 1\end{array}\right]$(6)

Where ${\tilde{a}}_{ij}$ is a fuzzy triangular number represented as ${\tilde{a}}_{ij}$ = ($l_{ij},m_{ij},u_{ij})$and ${{\tilde{a}}_{ij}}^{-1}=\left(\frac{1}{u_{ij}},\frac{1}{m_{ij}},\frac{1}{l_{ij}}\right)$. The membership function $\mu \tilde{a}\left(x\right)$ for TFN is a continuous mapping of real number $-\mathrm{\infty }\le x\le \mathrm{\infty }$ to the closed interval [0, 1] and can be represented by equation 1(1) ${\mu }_{\tilde{M}}=\left\{\begin{array}{c}0,x<a,\\ \frac{\left(x-a\right)}{\left(b-a\right)},a\le x\le b\\ \frac{\left(c-x\right)}{\left(c-x\right)},b\le x\le c\\ 0,x>c,\end{array}\right\}$(1) .

1. Calculate the fuzzy geometric mean value ${\tilde{r}}_i$

In the fuzzy comparison matrix, ${\tilde{r}}_i$ is calculated by multiplying the fuzzy numbers in a row as per the fuzzy multiplication rule and the n^th root is calculated for the establishment of the mean value.

3.4.3. Develop fuzzy weights of criteria

In this step fuzzy weights for every criterion is calculated by applying the equation

(7) ${\tilde{w}}_i={\tilde{r}}_i\otimes \left({\tilde{r}}_1\oplus {\tilde{r}}_2\oplus {\tilde{r}}_3\oplus \dots .\oplus {\tilde{r}}_n\right)-1$(7)

3.5. Fuzzy TOPSIS

TOPSIS (technique for order preference by similarity to an ideal solution) method has the fundamental principle of establishment of a positive ideal solution (PIS) and a negative ideal solution (NIS). Further, the geometric distance of each alternative form PIS and NIS is determined and the alternative with the shortest distance from PIS and farthest distance from NIS is selected.

3.5.1. Establish a decision matrix

In this step DM’s evaluate the supplier’s sustainability performance on sustainability criteria and mark their response using linguistic variables. DM’s mark their responses and corresponding fuzzy equivalent TFN are utilised for establishing the fuzzy decision matrix. As per Equation (8)(8) $\tilde{X}=\left(\begin{array}{ccccc}{\tilde{x}}_{11}& \cdots & {\tilde{x}}_{1j}& \cdots & {\tilde{x}}_{1n}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{i1}& \cdots & {\tilde{x}}_{ij}& \cdots & {\tilde{x}}_{in}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{m1}& \cdots & {\tilde{x}}_{mj}& \cdots & {\tilde{x}}_{mn}\end{array}\right);\cdot i=\overline{i,m},j=\overline{1,n}$(8)

(8) $\tilde{X}=\left(\begin{array}{ccccc}{\tilde{x}}_{11}& \cdots & {\tilde{x}}_{1j}& \cdots & {\tilde{x}}_{1n}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{i1}& \cdots & {\tilde{x}}_{ij}& \cdots & {\tilde{x}}_{in}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{m1}& \cdots & {\tilde{x}}_{mj}& \cdots & {\tilde{x}}_{mn}\end{array}\right);\cdot i=\overline{i,m},j=\overline{1,n}$(8)

Where: ${\tilde{x}}_{ij}$ represents the fuzzy value Performance of i^th alternative for j^th criteria.

3.5.2. Establish the combined fuzzy decision matrix

In this step, the fuzzy decision matrix of all the DM’s are combined to reach the final combined fuzzy decision matrix by

(9) ${\tilde{x}}_{ij}=(a_{ij},b_{ij},c_{ij})$(9)

Where $a_{ij}=\begin{array}{c}min\\ k\end{array}\left\{a_{ij}^k\right\}$, $b_{ij}=\frac{1}{k}{\sum }_{k=1}^k{b}_{ij}^k$, $c_{ij}=\begin{array}{c}max\\ k\end{array}\left\{c_{ij}^k\right\}$

3.5.3. Establish the normalised fuzzy decision matrix

The values of the combined decision matrix are normalised using the Equations (10)(10) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{\ast }},\frac{b_{ij}}{c_j^{\ast }},\frac{c_{ij}}{c_j^{\ast }}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot c_j^{\ast }=\begin{array}{c}max\\ i\end{array}\left\{c_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(10) and (11(11) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot a_j^{-}=\begin{array}{c}min\\ i\end{array}\left\{a_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(11) ). Equation (10)(10) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{\ast }},\frac{b_{ij}}{c_j^{\ast }},\frac{c_{ij}}{c_j^{\ast }}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot c_j^{\ast }=\begin{array}{c}max\\ i\end{array}\left\{c_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(10) is used when the criteria are beneficial criteria i.e. the higher values are preferred and Equation (11)(11) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot a_j^{-}=\begin{array}{c}min\\ i\end{array}\left\{a_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(11) is utilised for normalisation of non-beneficial criteria for which the lesser values are preferred.

(10) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{\ast }},\frac{b_{ij}}{c_j^{\ast }},\frac{c_{ij}}{c_j^{\ast }}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot c_j^{\ast }=\begin{array}{c}max\\ i\end{array}\left\{c_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(10)

(11) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot a_j^{-}=\begin{array}{c}min\\ i\end{array}\left\{a_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(11)

3.5.4. Establish the weighted normalised fuzzy decision matrix

In this step, the fuzzy weights of sub-criteria calculated using FAHP are multiplied with the normalised values using Equation (12)(12) ${\tilde{v}}_{ij}={\tilde{r}}_{ij}\times w_j$(12) according to the fuzzy multiplication rule shown in Table 3.

(12) ${\tilde{v}}_{ij}={\tilde{r}}_{ij}\times w_j$(12)

where $w_j$ represents the weight of the criteria

3.5.5. Calculate FPIS and FNIS

The fuzzy positive ideal solution (FPIS) $A^{\ast }$ and fuzzy negative ideal solution (FNIS) $A^{-}$ are calculated using Equation (13)(13) $A^{\ast }=\left({\tilde{V}}_1^{\ast },{\tilde{V}}_2^{\ast },\dots ..,{\tilde{V}}_n^{\ast }\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{\ast }=\cdot \begin{array}{c}max\\ i\end{array}\left(V_{ij3}\right)$(13) and Equation (14)(14) $A^{-}=\left({\tilde{V}}_1^{-},{\tilde{V}}_2^{-},\dots ..,{\tilde{V}}_n^{-}\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{-}=\cdot \begin{array}{c}min\\ i\end{array}\left(V_{ij1}\right)$(14) respectively.

(13) $A^{\ast }=\left({\tilde{V}}_1^{\ast },{\tilde{V}}_2^{\ast },\dots ..,{\tilde{V}}_n^{\ast }\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{\ast }=\cdot \begin{array}{c}max\\ i\end{array}\left(V_{ij3}\right)$(13)

(14) $A^{-}=\left({\tilde{V}}_1^{-},{\tilde{V}}_2^{-},\dots ..,{\tilde{V}}_n^{-}\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{-}=\cdot \begin{array}{c}min\\ i\end{array}\left(V_{ij1}\right)$(14)

3.5.6. Establish the distance from each alternative to FPIS and FNIS

In this step, the fuzzy distance of each alternative from FPIS and FNIS solutions are calculated using Equation (15)(15) $d_i^{\ast }={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{\ast }\right)$(15) and Equation (16)(16) $d_i^{-}={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{-}\right)$(16) respectively

(15) $d_i^{\ast }={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{\ast }\right)$(15)

(16) $d_i^{-}={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{-}\right)$(16)

3.5.7. Determine the relative closeness to the ideal solution

In this step, the fuzzy closeness distances to the FPIS and FNIS are considered simultaneously for calculating the relative closeness as per Equation.

(17) $c{c}_i=\frac{d_i^{-}}{d_i^{-}+d_i^{\ast }}$(17)

Step 7: Ranking of alternatives and selection:

In this step, SPI’s calculated through FIS and integrated fuzzy MCDM method are considered for awarding of final ranks to the potential suppliers. Appropriate weights as decided by DMs are given to FIS and MCDM approach and Cumulative SPI (CSPI) for each supplier is calculated. Based on the values of CSPI final ranks are awarded to all potential suppliers and the final selection of a sustainable supplier for awarding the contract can be made by the industry.

The flowchart of the proposed methodology has been shown in Figure (1).

Figure 1. Flow chart of proposed decision frame work

Figure 2. Triangular membership function

4. Application of the proposed methodology in case company

India is a fast developing country and stands at the fourth position in the world in terms of GDP. The iron and steel sector of India has contributed significantly to achieving this strong GDP position. Development in the railway sector, infrastructure, airports, oil &gas and steel demand in other sectors have resulted in the steel industry as the backbone of national growth. In 2005 India overtook the US to become the third-largest producer of crude steel. In a major achievement in January 2019 India, crude steel production reached 9.2 million tonnes (MT) and overtook Japan to become the second-largest producer in the world as reported by the World Steel Association. The Indian government is focusing much on the steel industry as it contributes 2% of the net GDP of the country and aims to increase its global share to 7.7 % by 2021.

Indian iron and steel industry is manufacturing rails, plates, bloom, billets, wires, rods, wheel, and axels, etc., and cater to the need for national and many international customers. India has the vision to become the global leader in crude steel production by increasing its steel production but at the same time is aware of the significance and necessity of achieving the sustainability objectives. Increased production will result in the enhancement of various steel making activities such as excavation of minerals from mines, search for new areas for raw materials, more emission of greenhouse gases, and disposal of wastes in water and land resulting in large scale impact over the environment. Hence the industry needs to expand its sustainability actions and in this regard need its suppliers to take up initiatives for achieving sustainability. Therefore the proposed methodology is implemented as a case study for an Indian iron and steel industry of central India.

The details of the application of the six steps of the proposed research methodology are:

Step 1: Formation of Decision-makers’ team:

At the initial stage, a team of decision-makers consisting of eight persons is formed. The team members selected, represents the top and middle management of the industry. The team members are selected from the departments which are associated with the supplier selection process in the industry. Hence, personnel from materials management, store management, finance, and quality control are considered for team formation and they have adequate experience in the industry have a thorough knowledge of the supplier selection process of the industry. Team members were personally contacted and prior consent of management and team members was taken for participating in the work. A meeting was held with all the decision-makers and a brief description was given to them about the role and responsibilities. The details of all the decision-makers of the team are presented in Table 4. The primary responsibility of the team comprises of identifying the potential suppliers and forming a pool from which the final selection can be made for contract allocation. Apart from this, the team is responsible for the finalisation of sustainability criteria specific for the industry and also contribute by providing timely responses in the decision-making process.

Table 4. Details of Decision maker’s team

Decision maker	Department	Designation	Experience in years
Decision maker 1	Materials management	Senior manager	13
Decision maker 2	Materials management	Deputy general manager	21
Decision maker 3	Materials management	Assistant general manager	17
Decision maker 4	Materials management	Manager	9
Decision maker 5	Materials management	Assistant general manager	17
Decision maker 6	Finance	Senior manager	13
Decision maker 7	Stores management	Assistant general manager	17
Decision maker 8	Quality control	Manager	9

Step 2: Review of Literature:

In the proposed framework the sustainability criteria proposed by Jain and Singh (2019) have been considered for developing the decision framework. In their work authors have performed a comprehensive literature survey for identification of sustainability criteria for SSS for a large scale industry. Authors have reported thirty-two criteria in the economic dimension and seventeen criteria in social and environmental dimensions respectively and have applied the fuzzy Kano model for criteria clustering.

Step 3: Sustainability criteria clustering:

Jain and Singh (2019) have clustered sustainability criteria into four main clusters: Must be, One dimensional, Indifferent and Attractive clusters. Further, authors have applied type IV Kano model for sub classifying sustainability criteria in the Attractive cluster into less attractive (A1), attractive (A2) and highly attractive (A3) criteria. Less Attractive (A₁) subcluster have been not considered for further analysis as being in ‘Less’ subclassification, it has low significance on SSS as compared to other two subclusters of Must be and Attractive clusters.

In this work sustainability criteria of Attractive and Highly Attractive clusters have been considered for further analysis (Table 5). In the next section, the sub-criteria classification has been carried out for the criteria under the Attractive cluster.

Table 5. Subclassified Attractive cluster sustainability criteria

Economic criteria	Attractive criteria
	Less attractive (A1)	Attractive (A2)	Highly attractive (A3)
	• Training Aid	• Warranties and claim policies	• Product development
	• Political situation	• Amount of past business	• JIT
		• Long term relationship	• Reciprocal arrangement
			• Packaging ability
Environmental criteria	• End of pipe	• Green	• Carbon footprint tax
	• Environmental training	warehousing	• Green transportation
Social criteria	• Society	• Wages	• Human resource capability

Step 4: Identification of sub-criteria of the selected cluster

The characteristic of Attractive criteria has been captured by establishing their sub-criteria based on current industrial practices, knowledge of DM’s, manufacturers, standards laid by national & international agencies. Further subclassification of these attractive sustainability criteria provides two-fold advantages to DM’s. Firstly the DM’s have deep insight knowledge of the criteria significance in SSS, prior to the establishment of sub-criteria. Secondly, DMs have to establish sub-criteria for lesser sustainability criteria and hence results are obtained in lesser time. For establishing the sub-criteria, a brainstorming session with decision-makers have been conducted and the Attractive sustainability criteria were presented to the DM’s with the objective of identification of sub-criteria and establishment of their evaluation levels. The team of decision-makers identified the sub-criteria based on the current supplier evaluation practices in the iron and steel industry.

For example, an Attractive cluster in economic dimension contains Warranties and claim policies (CA₁) which Blischke (1995) defined as ‘A Warranty is a seller’s assurance to a buyer that a product or service is or shall be as represented. It may be considered to be a contractual agreement between the buyer and seller (or manufacturer) which is entered into a sale of the product or service.’ To capture the different dimensions of Warranties and claim policies criteria DM’s have established two sub-criteria and their evaluation levels as:

1. Supplier recovery percentage (CA₁₁): This refers to the Supplier recovery/total warranty cost:-Supplier recovery claims are claims made by the manufacturer to the supplier for reimbursement for the warranty-related costs that are associated with a warranty claim or work order when the cause of the defect was a supplied part. As companies source, most of the components from suppliers, percentages of the warranty recovered from suppliers is a very important part of managing warranty costs and supplier quality. Supplier warranty and recovery amounts can help measure the supplier performance and help with discussions on parts pricing and warranty terms & conditions with suppliers.

2. Claim frequency (CA₁₂): It refers to the Number of Claims/Number of units. The industry can calculate the claim frequency by a number of claims or failures per thousand or million parts. A higher value of claim frequency is a matter of concern for the industry and should discuss it with the supplier.

Similarly, the Amount of past business (CA₂) is another sustainability criteria in the economic dimension which refers to the amount of past business that has been done with each vendor (Weber, Current, and Benton 1991). However, DM’s agreed upon evaluating the performance of the supplier by considering three sub-criteria.

1. The growth of net worth, the average of the last 3 years (CA₂₁): it is the increase in the value of the supplier’s net worth. It is calculated by taking the arithmetic mean of a series of net worth for a period of 3 consecutive years.

2. Profitability (before tax) (CA₂₂): Profit before tax (PBT) is a profitability measure that looks at a company’s profits before the company has to pay income tax. PBT is calculated by deducting all expenses from revenue which includes interest expenses and operating expenses except for income tax.

3. The average amount of business in the last 3 years (CA₂₃): It is defined as the average of the total amount of business that the industry has done with the supplier over the time span of the last three years. The higher value indicates much higher business transactions between the two parties and is considered as beneficial from supplier and industry perspective.

In the same manner, every criterion has been discussed by DM’s team and sub-criteria has been established for sustainability criteria in three dimensions (Table 6.). However, as sub-criteria may have a quantitative or qualitative nature hence it is difficult to fix a predefined range for the input variable. Therefore, depending on the nature of sub-criteria a range in the form of a minimum and maximum values are set for each evaluation level for each sub-criterion in the next step.

Table 6. Criteria, sub-criteria and quantification levels in three sustainability dimensions

Economic sustainability criteria
Attractive	Criteria	Sub-criteria	Best	Average	Worst
	Warranties and claim policies (CA1)	Supplier recovery percentage (CA11)	Supplier recovery percentage is more than 90 %	Supplier recovery percentage is more than 75 % but less than 90% percent	Supplier recovery percentage is more than 60 % but less than 75 % percent
		Claim frequency (CA12)	The claim frequency is 1 in 1 million considering six sigma model	Claim frequency is more than 1 but less than 3	Claim frequency is more than 3
	Amount of past business (CA2)	Growth of net worth, the average of the last 3 years (CA21)	Growth of net worth taking the average of the last 3 years is more than 25%	Growth of net worth taking the average of the last 3 years is more than 10% but less than 25%	Growth of net worth taking the average of the last 3 years is less than 10%.
		Profitability (before tax) (CA22)	Profitability (before tax) of the supplier is more than 20%	Profitability (before tax) of the supplier is more than 10% but less than 20%	Profitability (before tax) of the supplier is less than 10%.
		The average amount of business in the last 3 years (CA23)	The industry has done the business of more than 5% of the total business of the industry (as an average of last 3 years)	The industry has done the business of more than 2% but less than 5% (of the total business of the industry (as an average of last 3 years)	The industry has done the business of less than 2% of the total business of the industry (as an average of last 3 years)
	Long term relationship (CA3)	Duration of business association (CA3)	The supplier has more than 10 years of business relations with the industry and also contributes by participating in strategic decisions of the industry.	The supplier has more than 5 years but less than 10 years of business terms and performance level is as per standard norms of the industry.	The supplier is a new entrant and has less than 5 years of business relations with industry.
Highly Attractive	Product development (CHA1)	Degree Of Supplier Integration (CHA11)	Black box approach	Gray box approach	White box approach
		Time of Supplier Integration (CHA12)	Supplier integration is done at the idea generation stage of NPD	Supplier integration is done at the product/process service concept development stage	Supplier integration is done at the prototype building stage (last stage) of NPD.
	JIT (CHA2)	JIT Index	JIT index ranges from 1.0 to 1.02	JIT index ranges from 1.02 to 1.04	JIT index for the supplier is more than 1.04
	Reciprocal arrangement (CHA3)		Mutually reciprocal arrangement (The amount of reciprocal business is more than 15%)	Mutually reciprocal arrangement. (The amount of reciprocal business is more than 5% but less than 15%)	Mutually reciprocal arrangement. (The amount of reciprocal business is 5%)
	Packaging ability (CHA4)		The material used by the supplier for packaging is more than 40% but less than 100% reusable/recycle/biodegradable	The material used by the supplier for packaging is more than 20% but less than 40% reusable/recycle/biodegradable	The material used by the supplier for packaging is less than 20% reusable/recycle/biodegradable
Environmental sustainability criteria
Attractive	Green warehousing (EA1)	Lighting system (EA11)	The warehouse is having a balanced combination of natural sunlight and artificial lighting system and is controlled by automatic controls like motion and light sensors.	The warehouse has a balanced combination of natural and artificial alights but lack the automated controllers.	The warehouse does not have a proper lighting system.
		Water consumption (EA12)	The warehouse has implemented a water harvesting system and more than 80% percent water requirements are fulfilled by rainwater.	The warehouse has implemented a water harvesting system and more than 50% but less than 80% percent water requirements are fulfilled by rainwater.	The warehouse has implemented a water harvesting system and less than 50% percent water requirements are fulfilled by rainwater.
Highly Attractive	Carbon footprint tax (EA2)		The supplier has ISO 14,067:2018 certification	The supplier does not have an ISO 14,067:2018 within the time span of 1 year	The supplier does not have ISO 14,067:2018 and have not planned to obtain the certification in the next 3 years.
	Green transportation (EA3)		Supplier utilises more than 50% but less than 100% mode of green transport to supply the materials.	Supplier utilises more than 20% but less than 50% mode of green transport to supply the materials.	Supplier utilises less than 20% mode of green transport to supply the materials.
Social sustainability criteria
Attractive	Wages (SA1)		The probability that the supplier gives wages to the employees in accordance with the Minimum Wages Act, 1948 of the Indian constitution is between 90% to 100 %	The probability that the supplier gives wages to the employees in accordance with the Minimum Wages Act, 1948 of the Indian constitution is between 80% to 95%	The probability that the supplier gives wages to the employees in accordance with the Minimum Wages Act, 1948 of the Indian constitution is between 75% to 85 %
Highly Attractive	Human resource capability (SHA1)		The supplier has a code of conduct for SHRD and more than 15% of supplier’s employee have undergone training under SHRD	more than 5% but less than 15% of supplier’s employee have undergone training under SHRD	Less than 5% of the supplier’s employee has undergone training under SHRD

Step 5: Sustainability Performance Index (SPI) calculation through FIS

In this work three discrete FIS, each for economic, environmental and social dimensions has been developed for evaluating the supplier’s performance in each sustainability dimension. For each FIS, quantified evaluation levels of the sub-criteria act as the inputs for the FIS. Further, in FIS for economic and environmental dimension Attractive and Highly attractive sub-criteria have been handled separately for an in-depth evaluation of suppliers (Figure 3). The outputs of the three FIS are the performance index of the supplier in three sustainability dimensions.

1. Membership function and operational operators

Figure 3. FIS engines for sustainability criteria in economic, environmental and social dimensions

In the proposed FIS model triangular membership function has been used in all the three FIS engines. Further, three fuzzy sets have been applied for the input and output variables and the linguistic rating variables used are ‘Best’, ‘Average’, and ‘Worst’. However, for the evaluation of Performance Index in Economic Dimension (PIED), Performance Index in Social Dimension (PISD), and the Performance Index in Environmental Dimension (PIEND) of each supplier, five fuzzy sets of membership function has been considered and linguistic variables used are ‘extremely poor’, ‘poor’, ‘average’, ‘good’, and ‘very good’. In Figure 4 membership function with the associated linguistic rating for the evaluation of suppliers on sub-criteria has been presented. The membership function incorporated for the evaluation of PIED, PISD, and the PIEND with respective linguistic ratings have been shown in Figure 5.

• (b) Fuzzy rules (KM based) and Modified Architecture of FIS engine

Figure 4. Membership function for suppliers performance target range

Figure 5. Performance index target range

In this step, fuzzy rules are developed for all FIS using DM’s knowledge. A sample of rules extracted from the rule base of FIS for evaluation of supplier performance on Warranties and claim policies (CA₁) criteria has been presented in Table 7. Warranties and claim policy criteria have two sub-criteria (variables) (i) Supplier recovery percentage (CA₁₁) and (ii) Claim frequency (CA₁₂) having three membership functions, hence the number of rules to be framed are 9. Whereas criteria Amount of past business (CA₂) has three sub-criteria with three membership functions hence DM’s need to the frame (3³) 27 rules. However, in this work, re-architecting of the FIS engine has been done so as to reduce the number of rules to 9 (least possible rules). Similarly, FIS engines and fuzzy rules are established for all the criteria in the economic dimension. After framing of rules, the evaluation process of suppliers has been done by DM’s by judging on each sub-criteria (Table 8).

• (c) Defuzzification

Table 7. Rules examples from rule base for Warranties and claim policies criteria

Rule No.	Rules
Rule 1	If the supplier recovery percentage is Best AND claim frequency is Best then the output is Best
Rule 2	If the supplier recovery percentage is Best AND claim frequency is Average then the output is Best
Rule 3	If the supplier recovery percentage is Best AND claim frequency is Worst then the output is Average
Rule 4	If the supplier recovery percentage is Average AND claim frequency is Best then the output is Best
Rule 5	If the supplier recovery percentage is Average AND claim frequency is Best then the output is Average
Rule 6	If the supplier recovery percentage is Average AND claim frequency is Worst then the output is Worst
Rule 7	If the supplier recovery percentage is Worst AND claim frequency is Best then the output is Average
Rule 8	If the supplier recovery percentage is Worst AND claim frequency is Best then the output is Worst
Rule 9	If the supplier recovery percentage is Worst AND claim frequency is Best then the output is Worst

Table 8. Suppliers assessment values for criteria and sub-criteria by decision makers

Economic criteria
Attractive	Criteria	Sub-criteria	Supplier 1	Supplier 2	Supplier 3	Supplier 4
	Warranties and claim policies (CA1)	Supplier recovery percentage (CA11)	75	90	65	80
		Claim frequency (CA12)	5	1	4	2
	Amount of past business (CA2)	The growth of net worth, the average of the last 3 years (CA21)	20	24	10	15
		Profitability (before tax) (CA22)	10	19	15	10
		The average amount of business in the last 3 years (CA23)	2	5	2	3
	Long term relationship (CA3)	Duration of business association (CA3)	5	10	8	6
Highly Attractive	Product development (CHA1)	Degree Of Supplier Integration (CHA11)	8	10	5	9
		Time of Supplier Integration (CHA12)	5	9	5	2
	JIT (CHA2)	JIT Index	1.02	1.01	1.04	1.0
	Reciprocal arrangement (CHA3)		5	13	11	12
	Packaging ability (CHA4)		10	70	60	90
Environmental criteria
Attractive	Green warehousing (EA1)	Lighting system (EA11)	1	9	7	6
		Water consumption (EA12)	10	90	50	70
Highly Attractive	Carbon footprint tax (EA2)		2	8	5	5
	Green transportation (EA3)		10	70	10	10
Social Criteria
Attractive	Wages (SA1)		85	85	75	95
Highly Attractive	Human resource capability (SHA1)		12	12	5	14

The output of the three distinct FIS is the fuzzified values of performance index in the respective sustainability dimension. Defuzzification of these values has been done by the Centre of Area (COM) method (Eq 3)(3) $x_{COA}=\frac{{\sum }_{i=1}^n{x}_i{\mu }_i\left(x_i\right)}{{\sum }_{i=1}^n{\mu }_i\left(x_i\right)}$(3) and corresponding crisp values have been obtained. The defuzzified values of PIED, PISD and the PIEND have been tabulated in Table 9. Based on the values of PIED, it elicits that for the economic dimension, supplier 2 has the highest performance level followed by supplier 3 and the lowest performance is marked by supplier 1. PIEND is highest for supplier 2 and has the best performance level and supplier 1 has the lowest performance level for the environmental dimension. PISD of supplier 2 is highest and supplier 1 has the least PISD indicating the best and lowest performance levels of the suppliers respectively. After carrying out discussions, DMs assigned weights as 0.5, 0.3 and 0.2 to economic, environmental and social dimensions respectively. Further using Eq. 4(4) $SPI={\sum }^{\left\{(W_{economic}\ast PIED)+\left(W_{social}\ast PISD\right)+\left(W_{environmental}\ast PIEND\right)\right\}}$(4) SPI of each supplier is calculated and based on SPI ranks are awarded to suppliers. FIS methodology yields, top rank to supplier 2 followed by supplier4 and supplier 3 and last rank is awarded to supplier 1.

Table 9. Performance index values in three susinability dimensions through FIS

	Performance index in the economic dimension (PIED)			Performance index in Environmental Dimension (PIEND)			Performance index in Social Dimension (PISD)
Supplier	Calculated values	Normalised values	Ranks	Calculated values	Normalised values	Ranks	Calculated values	Normalised values		Ranks	SPI	Overall Ranks
1	3.999	0.1573	4	2.0827	0.1016	4	1.564		0.081	3	0.12534	4
2	8.917	0.3509	1	8.9083	0.4347	1	7.725		0.401	2	0.38608	1
3	7	0.2754	2	5.5	0.2684	2	1.489		0.077	4	0.23363	3
4	5.5	0.2164	3	3.9995	0.1951	3	8.47		0.44	1	0.25476	2

Step 6: Sustainability Performance Index (SPI) calculation through an integrated fuzzy MCDM method.

In this step, fuzzy integrated MCDM methods have been applied for finding the SPI of suppliers. Fuzzy AHP method has been utilised for finding the weights of the criteria and their respective sub-criteria. Further, utilising these weights, the Fuzzy TOPSIS method has been applied for the assessment of the potential suppliers and determination of SPI.

4.1. Fuzzy AHP

Foremost, DM’s perform the pairwise comparison of the criteria and sub-criteria in all sustainability dimensions and assign the priority weights to each dimension. The linguistic response and its corresponding fuzzified scale used by DM’s is shown in Table 10. The results of the comparison are established in a pairwise comparison matrix. Further, consistency ratio (CR) for all the criteria in economic, environmental and social dimensions have been calculated using Equation (5)(5) $CF=\frac{\left({\lambda }_{max}-1\right)}{\left(n-1\right)}$(5) and has been verified as less than 0.01. The linguistic response of DM’s are converted into the corresponding TFN equivalent as shown in Table 10 and a fuzzy judgement matrix has been established in this step using Equation (6)(6) $\tilde{A}=\left[\begin{array}{cccc}1& {\tilde{a}}_{12}& \cdots & {\tilde{a}}_{1n}\\ {\tilde{a}}_{21}& 1& \cdots & {\tilde{a}}_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ {\tilde{a}}_{n1}& {\tilde{a}}_{n2}& \cdots & 1\end{array}\right]$(6) . After establishing the fuzzy judgement matrix, applying the fuzzy multiplication rule as per Table 3 calculations have been performed and the geometric mean values for all sustainability criteria and sub-criteria are established. Thereafter, fuzzy weights have been computed for all sustainability criteria and sub-criteria using Equation (7)(7) ${\tilde{w}}_i={\tilde{r}}_i\otimes \left({\tilde{r}}_1\oplus {\tilde{r}}_2\oplus {\tilde{r}}_3\oplus \dots .\oplus {\tilde{r}}_n\right)-1$(7) . Applying Equation (7)(7) ${\tilde{w}}_i={\tilde{r}}_i\otimes \left({\tilde{r}}_1\oplus {\tilde{r}}_2\oplus {\tilde{r}}_3\oplus \dots .\oplus {\tilde{r}}_n\right)-1$(7) the priority weights of the Attractive subcluster have been established as 0.33337 and for the Highly attractive subcluster is established as 0.66667. The CR, priority weights and fuzzified weights for Attractive subcluster in economic dimension have been shown in Table 11. Similarly, priority weights and fuzzified weights for criteria and sub-criteria under environmental and social dimensions have been established. The local and global weights of sustainability criteria in each dimension has been presented in Table 12.

Table 10. Fuzzy scale for AHP and TOPSIS

Level of importance (aij)	Linguistic response	The linguistic definition for comparison of the i^th and the j^th items	Fuzzy scale (l,m,u)
1	Very Low (VL)	The i^th item is equally important as the j^th item	(1,1,1)
3	Low (L)	The i^th item is slightly more important than the j^th item	(2,3,4)
5	Average (A)	The i^th item is more important than the j^th item	(4,5,6)
7	High(H)	The i^th item is strongly more important than the j^th item	(6,7,8)
9	Very High (VH)	The i^th item is extremely more important than the j^th item	(9,9,9)
The intermediate values between two adjacent judgements
2			(1,2,3)
4			(3,4,5)
6			(5,6,7)
8			(7,8,9)
1/aij = aji	The inverse comparison between the i^th and the j^th items		($\frac{1}{u},1\text{overm},\frac{1}{l}$)

Table 11. Priority weighs for attractive economic criteria

					fuzzified weights
	Warranties and claim policies (CA1)	Amount of past business (CA2)	Long term relationship (CA3)	Priority weights	l	m	u
Warranties and claim policies (CA1)	1	5	7	0.7235060	0.560	0.731	0.934
Amount of past business (CA2)	0.20	1	3	0.1931860	0.135	0.188	0.277
Long term relationship (CA3)	0.142857143	0.333333333	1	0.0833078	0.061	0.081	0.112
ʎ max = 3.065819	CI = 0.0329	RI = 0.58	CR = 0.0567402

Table 12. Global weights of sustainability criteria and sub-criteria by FAHP method

Economic criteria
Attractive	Criteria	Local weights			Sub-criteria	Local Weights			Global Weights
	Warranties and claim policies (CA1)	0.56	0.731	0.934	Supplier recovery percentage (CA11)	0.678	0.833	1.017	0.0615	0.1633	0.3953
					Claim frequency (CA12)	0.138	0.167	0.208	0.01354	0.03200	0.07247
	Amount of past business (CA2)	0.135	0.188	0.277	Growth of net worth, the average of last 3 years (CA21)	0.154	0.223	0.324	0.02599	0.06733	0.16142
					Profitability (before tax) (CA22)	0.061	0.081	0.112	0.0615	0.1633	0.3953
					The average amount of business in the last 3 years (CA23)	0.445	0.616	0.816	0.0615	0.1633	0.3953
	Long term relationship (CA3)	0.061	0.081	0.112					0.01354	0.03200	0.07247
Highly Attractive	Product development (CHA1)	0.455	0.607	0.796	Degree Of Supplier Integration (CHA11)	0.522	0.750	1.045	0.0869	0.3035	0.9134
					Time of supplier Integration (CHA12)	0.185	0.250	0.369	0.0308	0.1012	0.3225
	JIT (CHA2)	0.168	0.245	0.36	JIT Index				0.0615	0.1633	0.3953
	Reciprocal arrangement (CHA3)	0.037	0.048	0.066					0.01354	0.03200	0.07247
	Packaging ability (CHA4)	0.071	0.101	0.147					0.02599	0.06733	0.16142
Environmental
Attractive	Green warehousing (EA1)	1	1	1	Lighting system (EA11)	0.678	0.833	1.017	0.1433	0.2777	0.6448
					Water consumption (EA12)	0.138	0.167	0.208	0.0292	0.0557	0.1319
Highly Attractive	Carbon footprint tax (EA2)	0.757	0.875	1.009					0.2771	0.5833	1.1080
	Green transportation (EA3)	0.109	0.125	0.146					0.0399	0.0833	0.1603
SOCIAL
Attractive	Wages (SA1)	1	1	1					0.211323	0.333333	0.633976
Highly Attractive	Human resource capability (SHA1)	1	1	1					0.366024	0.666667	1.098084

4.2. FTOPSIS

At the beginning of FTOPSIS technique, DM’s mark their responses using linguistic variables available as per Table 10.nthe response of DM’s are changed to corresponding fuzzy equivalent TFN and the fuzzy decision matrix is established as per Equation (8)(8) $\tilde{X}=\left(\begin{array}{ccccc}{\tilde{x}}_{11}& \cdots & {\tilde{x}}_{1j}& \cdots & {\tilde{x}}_{1n}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{i1}& \cdots & {\tilde{x}}_{ij}& \cdots & {\tilde{x}}_{in}\\ ⋮& \ddots & ⋮& \ddots & ⋮\\ {\tilde{x}}_{m1}& \cdots & {\tilde{x}}_{mj}& \cdots & {\tilde{x}}_{mn}\end{array}\right);\cdot i=\overline{i,m},j=\overline{1,n}$(8) . Further, incorporating the responses of all decision-makers a final combined fuzzy decision matrix is established using Equation (9)(9) ${\tilde{x}}_{ij}=(a_{ij},b_{ij},c_{ij})$(9) . After the establishment of the combined fuzzy decision matrix, the values of the matrix are normalised using the Equations (10)(10) ${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{\ast }},\frac{b_{ij}}{c_j^{\ast }},\frac{c_{ij}}{c_j^{\ast }}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot c_j^{\ast }=\begin{array}{c}max\\ i\end{array}\left\{c_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(10) and (11(11) ${\tilde{r}}_{ij}=\left(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}}\right)\cdot \mathrm{a}\mathrm{n}\mathrm{d}\cdot a_j^{-}=\begin{array}{c}min\\ i\end{array}\left\{a_{ij}\right\}\cdot \mathrm{f}\mathrm{o}\mathrm{r}\cdot \mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\cdot \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}$(11) ). All the sub-criteria except Claim frequency and Time of supplier integration are the non-beneficial sub-criteria. As a next step, the fuzzy weights of sub-criteria calculated using FAHP are multiplied with the normalised values using Equation (12)(12) ${\tilde{v}}_{ij}={\tilde{r}}_{ij}\times w_j$(12) according to the fuzzy multiplication rule shown in Table 3. Further, (FPIS) $A^{\ast }$ and (FNIS) $A^{-}$ are calculated using Equation (13)(13) $A^{\ast }=\left({\tilde{V}}_1^{\ast },{\tilde{V}}_2^{\ast },\dots ..,{\tilde{V}}_n^{\ast }\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{\ast }=\cdot \begin{array}{c}max\\ i\end{array}\left(V_{ij3}\right)$(13) and Equation (14)(14) $A^{-}=\left({\tilde{V}}_1^{-},{\tilde{V}}_2^{-},\dots ..,{\tilde{V}}_n^{-}\right)\cdot \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\cdot {\tilde{V}}_j^{-}=\cdot \begin{array}{c}min\\ i\end{array}\left(V_{ij1}\right)$(14) respectively for sub-criteria in each sustainability dimensions separately. Then the fuzzy distance of each alternative from FPIS and FNIS solutions are calculated using Equation (15)(15) $d_i^{\ast }={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{\ast }\right)$(15) and Equation (16)(16) $d_i^{-}={\sum }_{j=1}^{n}d\left({\tilde{V}}_{ij},{\tilde{V}}_j^{-}\right)$(16) respectively in each sustainability dimension and results have been presented in Table 13. Applying Equation (17)(17) $c{c}_i=\frac{d_i^{-}}{d_i^{-}+d_i^{\ast }}$(17) the relative closeness for all suppliers has been calculated in each sustainability dimension and has been shown in Table 13. The closeness coefficient in the economic dimension represents the supplier’s performance index in the economic dimension (PIED). Similarly, closeness coefficient values of the environmental and social domains are a representation of the performance index in the environmental dimension (PIEND) and social dimension (PISD) respectively. For establishing SPI of each supplier through an integrated FMCDM approach, DMs have decided the weight of the economic dimension as 0.5, for the environmental dimension as 0.3 and for the social dimension as 0.2. Considering these weights SPI of each supplier has been calculated using Equation 4(4) $SPI={\sum }^{\left\{(W_{economic}\ast PIED)+\left(W_{social}\ast PISD\right)+\left(W_{environmental}\ast PIEND\right)\right\}}$(4) . Calculated SPI values and normalised SPI values are presented in Table 13.

Table 13. SPI values of sustainability dimension through fuzzy TOPSIS

		SUPPLIER 1	SUPPLIER 2	SUPPLIER 3	SUPPLIER 4
Economic	Di*	0.3141	0.1280	0.2796	0.1405
	Di^−	0.1406	0.3115	0.1997	0.3070
	CCi (PIED)	0.3093	0.7088	0.4166	0.6859
	Normalised (PIED)	0.1458	0.3342	0.1965	0.3235
RANKS	4	1	3	2
Environmental	Di*	0.2204	0.1025	0.1384	0.1244
	Di^−	0.1030	0.2049	0.1046	0.2916
	CCi (PIEND)	0.3185	0.6666	0.4304	0.7010
	Normalised (PIEND)	0.1505	0.3150	0.2034	0.3312
	RANKS	4	2	3	1
Social	Di*	0.3455	0.1548	0.2493	0.0481
	Di^−	0.0325	0.2851	0.1906	0.3583
	CCi (PISD)	0.0861	0.6481	0.4332	0.8816
	Normalised (PISD)	0.0420	0.3163	0.2114	0.4303
	RANKS	4	2	3	1
SPI through fuzzy MCDM		0.1265	0.3249	0.2015	0.3471
Overall Ranks		4	2	3	1

Step 7: Ranking of alternatives and selection:

In this step, the SPI of each supplier from FIS and integrated FMCDM approaches are compared for determining the final ranks of suppliers. After holding a discussion with DM’s it was decided to award equal weights (0.5) to SPI established by FIS and integrated FMCDM approaches respectively. Calculations were performed accordingly and the final SPI is calculated and based on the normalised SPI values, final ranks are awarded to the potential suppliers (Table 14).

Table 14. Final ranks of the suppliers

	SPI by FIS approach	SPI by Integrated fuzzy MCDM approach	Calculated SPI	Final Ranks
Supplier 1	0.12534	0.126468	0.1259	4
Supplier 2	0.38608	0.32486	0.3555	1
Supplier 3	0.23363	0.201527	0.2176	3
Supplier 4	0.25476	0.347145	0.3010	2

The top rank is attained by supplier 2 followed by supplier 4 and the last rank has been awarded to supplier 1.

5. Discussions

5.1. Sustainability criteria and sub-criteria

In the economic dimension, Warranties and claim policy criteria have been addressed by two sub-criteria. Iron and steel sector is a large scale industry and employs expensive, automatic and high-end machinery in its manufacturing process. Hence industry is delighted to have an apt warranty attached to machinery and material supplied by the supplier. Further, the efficient, simple, transparent, automated and fast claim process is desired by industry and if any supplier is offering such a claim process to the industry then the satisfaction level of the industry is enhanced. Large Amount of past business by the supplier adds to the image building of the supplier. The high amount of business also helps the supplier in developing a favourable feeling of mutual trust between supplier and industry which makes the supplier more reliable. Trusted suppliers enable organisations to outsource their non-critical activities, thus reducing internal workloads and increasing efficiencies. The industry tends to establish a strong, mutually beneficial long-term relationship with suppliers as it helps in improving sustainability performance across the supply chain, generating greater cost efficiency and also helps in the growth of the business. Further in large scale industries initial set up costs are substantial and time-consuming. But suppliers with a long association can help to offset these costs by eliminating re-tendering and renegotiation costs. Moreover, long term relationship with suppliers also provides an opportunity to industry for engaging the engage suppliers in the process of product development, development of new processes.

In Highly attractive subcluster, product development sub-criteria are of vital importance for industries. iron and steel industries have to cater to the need of new projects for which they have to develop new products. As supplier’s participation in product development projects helps to reduce the cost, improve the quality, and also provide innovative technologies (Handfield et al. 1999). Petersen, Handfield, and Ragatz (2005) have also reported that suppliers may be involved at different stages of the new product development process. Early supplier involvement is a key coordinating process in supply chain design, product design and process design (Gentry and Savitskie 2008).

To compete in the global market and to withstand tough competition from its counterparts steel sector must maintain its competitive advantage. The essence of establishing a permanent competitive advantage demands the creation of value between customers through providing quality products at an acceptable cost. For this industry needs to eliminate in valued activities and maintain the least possible inventories. Therefore just in time (JIT) production system is highly desired criteria for the industry.

In the environmental dimension, ‘green warehousing’ is clustered as attractive sub-classification as supplier’s ability to maintain green warehouses helps the industry to achieve its sustainability objectives. However ‘Carbon footprint tax’ is under a highly attractive sub-cluster because the lesser carbon tax is economically beneficial and also significant in conserving the environment. Adoption of ‘Green transportation’ means by suppliers helps the industry to reduce carbon footprint tax hence is a highly attractive criterion.

In the social dimension ‘Wages’ has been subclassified as Attractive criteria and ’Human resource policy’ as Highly attractive criteria, Industry desire that the suppliers should pay salary to the employees as per the norms of government because Non-Compliance to the salary norms by suppliers can adversely affect the sustainability image of the parent organisation. Further, the industry is delighted to associate with suppliers who have a provision for providing training on sustainability issues to all employees, encourages its employees for participation in quality and sustainability improvement initiatives.

5.2. FIS and fuzzy MCDM approach

The SPI values established through the FIS approach (Table 9) elicit that supplier 2 has good performance in economic and environmental dimensions but in social dimension supplier 4 has better performance. However, supplier 2 has the highest SPI and secure overall top rank among the four suppliers. Supplier 3 has performed well in economic and environmental dimension but has poor performance in social dimension and have secured the third rank. On the other hand supplier, 2 has lower performance in economic and environmental dimensions but has superior performance in the social dimension and manages to reach the second rank. Suppliers ranking based on the SPI values through FIS are S2 > S4>S3>S1.

The SPI values through the fuzzy MCDM approach (Table 13) tells that supplier 2 is having the best performance in economic dimension and supplier 1 performance is lowest. However, in environmental and social dimension supplier 1 outperforms and supplier 4 has again the poorest performance in both the sustainability dimensions. Based on the SPI values through the fuzzy MCDM approach the final ranking of suppliers is S4 >S2>S3>S1. It is elicited from the results of both approaches that first and second ranks have been changed however, the third and fourth ranks are the same.

The evaluated ranks of suppliers by the FIS and fuzzy MCDM approach in each sustainability dimension are presented in Table 15. It elicits that the ranks of suppliers as established by both approaches are varying due to their inherent characteristics. In economic dimension ranks of supplier 1 and supplier 2 are the same but the ranks of supplier 3 and supplier 4 are reversed. In the environmental dimension except supplier 4, the ranks of all suppliers are different. Similarly, in social dimension supplier, 1 and supplier 3 ranks are reversed and supplier 4 and supplier 2 have no change in their ranks. The overall ranks established on SPI values of FIS and fuzzy MCDM approaches have a significant variation in the ranks of suppliers. FIS approach awards first rank to supplier 2 whereas as per the fuzzy MCDM approach supplier 4 is top-ranked. Further, As per the FIS approach supplier, 4 is having the second rank whereas the fuzzy MCDM approach awards supplier 2 with this rank. In the final awarding of ranks, supplier 2 tops the list with first rank and supplier 4 is having the second rank, supplier 3 has the third rank and supplier 1 is having the last ranking.

Table 15. Ranks position for suppliers

	Economic Dimension		Environmental Dimension		Social Dimension		Overall ranks		Final Ranks
Supplier	FIS	Fuzzy MCDM	FIS	Fuzzy MCDM	FIS	Fuzzy MCDM	FIS	Fuzzy MCDM
1	4	4	4	4	3	4	4	4	4
2	1	1	1	2	2	2	1	2	1
3	2	3	2	3	4	3	3	3	3
4	3	2	3	1	1	1	2	1	2

6. Managerial implications

The proposed SSS framework has many managerial practical implications for supply chain managers. Firstly, the proposed decision model for SSS provides managers with a framework for the SSS by evaluating the supplier’s performance on Attractive and Highly attractive criteria in three sustainability dimensions. Secondly, the proposed framework provides a common platform to consider the results of both, FIS and the fuzzy MCDM approach in a sustainability environment for evaluating the sustainability performance of potential suppliers. Thirdly, the methodology also provides deep insight into the level of perceived satisfaction by industry through the SSS process by considering sub-classified Attractive criteria. The practical application of the proposed framework in the industry helps DMs in achieving the sustainability objectives of the industry and also helps in attaining the highest level of satisfaction from the SSS process. Further, the proposed model incorporates the knowledge of managers and experts of the industry to improve the effectiveness of the SSS process and allows them to have a detailed insight into the sustainability performance of suppliers. The proposed framework considers the results of FIS and fuzzy MCDM techniques for supplier evaluation, providing more efficient and reliable results that allow the DMs to develop an effective and efficient selection process. Further, sharing and discussing the SPI values with suppliers, managers can provide the necessary inputs to help the suppliers to improve their sustainability performance. The proposed model incorporates twelve sustainability criteria and nine sub-criteria of a large scale industry. However, the framework is adaptable to incorporate different criteria and sub-criteria of other industries as per the need.

7. Conclusions and future work

Sustainable suppliers are key players in facilitating industries to attain their sustainability objectives of the supply chain. Therefore the selection of sustainable suppliers is a vital decision for industries. The present methodology provides a supplier selection framework by integrating the FIS and fuzzy MCDM approaches in the sustainability horizon. The framework incorporates Attractive and Highly Attractive sustainability criteria for sustainability performance evaluation and enhancement of perceived satisfaction by industry. The attractive cluster encompasses nine criteria in the economic dimension, five criteria under the environmental dimension and three criteria under the social dimension. Further, eight sub-criteria in economic dimension and two sub-criteria in the environmental dimension have been established and these act as an input for the FIS system and integrated fuzzy MCDM techniques respectively. SPI obtained from both approaches in the sustainability paradigm is utilised to develop a decision framework for selecting sustainable suppliers for contract allocation. The proposed methodology integrates FIS and fuzzy MCDM approaches on the sustainability platform, however, the supply chain managers can apply these approaches distinctively depending on the nature of the sustainability criteria. Managers can apply the fuzzy MCDM approach when the quantified criteria and sub-criteria are available for decision making and can utilise the FIS approach when decision framework incorporates criteria and sub-criteria of qualitative nature.

This approach has been validated by the iron and steel industry as a case company. The results of the work provide a deep insight into the performance of every supplier in each sustainability dimension. Further, the SPI of the supplier provides a means to SCM managers for taking the decision of contract allocation. SCM managers can share the results with suppliers and suppliers can self-assess their performance on sustainability dimensions and can focus on improving their sustainability performance.

The proposed model for SSS has some limitations also. Firstly, the proposed model is based on Mamdani FIS and the results significantly depend on a set of rules framed by DM’s based on their personal experience and knowledge. The number of rules increases drastically in increasing the number of inputs to FIS. Another limitation of the present work is that it incorporates the sustainability criteria relevant to the iron and steel industry of India only. Hence as future proposed work, the supply chain managers representing other industries are encouraged to develop a more comprehensive list of sustainability criteria. Further, researchers are encouraged to examine the interrelationship between sustainability criteria and their sub-criteria using ANP. As a proposed future research work, academicians and researchers can take up the task of developing a mathematical model for order allocation to selected suppliers considering the constraints in each sustainability dimension.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Naveen Jain

Naveen Jain is a research scholar at Mechanical Engineering department of National Institute of Technology, Raipur, India. He has completed his Bachelor of Engineering in Mechanical Engineering from Barkatullah University; Bhopal, India. He holds Masters in Production Engineering. His research areas are sustainability, sustainable supply chain management, multi criteria decision making and optimization. He has published papers in International and national journals and has presented papers in International conferences.

A. R. Singh

Dr. A. R. Singh is Asssistant Professor in the Mechanical Engineering department of National Institute of Technology, Raipur, India. He completed his Bachelor of Engineering degree in Mechanical engineering from U.P.T.U, University. He has Master of Technology degree in Production Engineering from Motilal Nehru National Institute of Technology, Allahabad, India. He holds a PhD in Mechanical Engineering from Motilal Nehru National Institute of Technology, Allahabad, India. His areas of specialization are operation research, supply chain management, optimization techniques and multi criteria decision making. He has published many papers in International journals. Some of the international journals in which papers are published include – International Journal of Advanced Manufacturing Technology, International journal of multi criteria decision making, Journal of intelligent manufacturing, International Journal of Design Engineering, International journal of manufacturing systems, Applied Mathematics and Computation.

R. K. Upadhyay

Dr. R. K. Upadhyay has served as a Professor in Mechanical Engg Department at Anand Engineering College Agra and as Faculty Member in Department of Mechanical Engg, DEI, Dayalbagh, Agra. He is an Academic Veteran, Technocrat cum Researcher, Mentor and Practicing Entrepreneurship Facilitator with demonstrated history of working actively in the area of Subconscious and Emotional Intelligence, Peace of Mind, Motivation and Effective problem solving at workplaces. He has conducted many interesting and thought provoking sessions for students, parents, educational institutes and corporate sectors. Additionally, he has delivered brainstorming session on cutting-edge technologies Industry 4.0 which comprises of smart manufacturing, mixed reality and automotive manufacturing. Dr. Upadhyay is also a renowned author, His books on Workshop Practice (2001) and Manufacturing Science (2004) were highly appreciated by student’s community of U.P.T.U. (now A.K.T.U.) Lucknow.