TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environ
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TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment Kamal Kumar1 · Harish Garg1
Received: 3 September 2016 / Revised: 11 November 2016 / Accepted: 12 November 2016 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016
Abstract The objective of this paper is to focus on multi-attribute decision-making for interval-valued intuitionistic fuzzy set environment based on set pair analysis (SPA). For it, the major component of the SPA known as connection number has been constructed based on the set pairs between two preference values consists of every attribute and ideal pairs of it. Based on these connection numbers, an extension of technique for order of preference by similarity to ideal solution method is developed by combining the proposed connection number for IVIFSs and hence finding the best alternative(s) using relative degree of closeness coefficient. An illustrative example has been given for demonstrating the approach and compares their performance with some existing measures. Keywords Set pair analysis · Connection number · Interval-valued intuitionistic fuzzy set · Decision-making Mathematics Subject Classification 03B52 · 03E72 · 90B50 · 90C70
1 Introduction Multiple attribute decision-making (MADM) problems are the important parts of modern decision theory due to the rapid development of economic and social uncertainties. In a decision-making problem, we have a set of different alternatives to solve the problem and a set of decision makers, which are usually required to furnish their preference values about the alternatives. To get the group’s opinions about the alternatives, aggregation techniques are required for aggregation of all the information. During the last few years, more and more
Communicated by Rosana Sueli da Motta Jafelice.
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Harish Garg [email protected] http://sites.google.com/site/harishg58iitr/ School of Mathematics, Thapar University, Patiala, Punjab 147004, India
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K. Kumar, H. Garg
researchers are paying attentions to aggregate the different opinions under the intuitionistic fuzzy set (IFS) (Atanassov 1986) or interval-valued IFS (IVIFS) (Atanassov and Gargov 1989) and hence many aggregation operators for IFSs/IVIFS have been developed (Garg 2016d; Xu and Yager 2006; Xu 2007; Garg 2016c, e; Wei et al. 2011; Garg 2016b). However, apart from that Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), developed by Hwang and Yoon (1981), is a well-known multi-criteria decision-making (MCDM) method. The basic features of this method are chosen the alternative in such a way that they have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. After their existence, many researchers are paying more attention on it and have widely applied in fuzzy multi-attribute decision-making problems. Chen (2000) extended the TOPSIS approach to fuzzy decision-making by defining the crisp Euclidean distance between t
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