Multi-criteria COPRAS Method Based on Parametric Measures for Intuitionistic Fuzzy Sets: Application of Green Supplier S
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RESEARCH PAPER
Multi-criteria COPRAS Method Based on Parametric Measures for Intuitionistic Fuzzy Sets: Application of Green Supplier Selection Reetu Kumari1 • Arunodaya Raj Mishra2 Received: 20 September 2018 / Accepted: 13 January 2020 Shiraz University 2020
Abstract In this manuscript, we present complex proportional assessment (COPRAS) method to solve multi-criteria decision-making (MCDM) problems with intuitionistic fuzzy information, known as IF-COPRAS method. In this method, a new formula is developed to evaluate the criterion weights, in which the objective weights are calculated from divergence measure method. For this, new parametric divergence and entropy measures are investigated and some desirable properties are also discussed. Since the vagueness or uncertainty is an unavoidable characteristic of MCDM problems, the proposed approach can be a useful tool for decision making in an uncertain atmosphere. Further, a decision-making problem of green supplier selection is presented to demonstrate the usefulness of the proposed method. To illustrate the validity of the proposed method, comparison with existing methods is presented and the stability is also discussed through a sensitivity analysis with different values of criterion weights. Keywords Entropy Divergence measure Intuitionistic fuzzy sets Complex proportional assessment (COPRAS) Green supplier
1 Introduction Green supply chain management (GSCM) is a policy which reinforces and incorporates the environmental concern into entire supply chain process. Due to increasing environmental issues, several researchers and practitioners have paid attention on GSCM. As the green supplier alternatives influenced by many criteria, it is assumed as an MCDM problem. In the supplier selection, it is not always possible to determine an efficient solution due to inaccurate decision information. The doctrine of fuzzy sets (FSs) pioneered by Zadeh (1965) have widely received attention from decision makers in the procedure of decision making. On the last & Arunodaya Raj Mishra [email protected] Reetu Kumari [email protected] 1
Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP 473226, India
2
Department of Mathematics, Govt. College Jaitwara, Satna, MP, India
two decades, various approaches and doctrines for dealing vagueness and uncertainty have been introduced. Later on, a variety of extensions of FSs have been pioneered. In FSs, the membership of an element is defined to be a number from the interval [0, 1] and the non-membership is simply its complement. But, in reality, this hypothesis does not match with human intuition. To evade the shortcomings of FSs, Atanassov (1986) extended the concept of FSs to intuitionistic fuzzy sets (IFSs) by extending a single membership function into three functions: the membership, the non-membership and the hesitation function such that the addition of the membership and non-membership values is less than or equal to one (Mishra 2016; Mishra et al. 2017a). As the IFSs ha
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