A robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces

The purpose of this study is to introduce an innovative multi-attribute group decision making (MAGDM) based on bipolar fuzzy set (BFS) by unifying“ VIseKriterijumska Optimizacija I Kompromisno Rasenje (VIKOR)” method. The VIKOR method is considered to be a useful MAGDM method, specifically in conditions where an expert is unable to determine his choice correctly at the initiation of designing a system. The method of VIKOR is suitable for problems containing conflicting attributes, with an assumption that compromising is admissible for conflict decision, the expert wishes a solution very near to the best, and the different alternatives or choices are processed according to all developed attributes. The theory of set pair analysis is a state-of-the-art uncertainty theory which consists of three factors, including “identity degree”, “discrepancy degree”, and “contrary degree” of connection numbers (CNs) and coincidence with many existing theories dealing with vagueness in the given information. Consequently, inspired by this, in the present study, we make an effort to improve the theory of data measurement by introducing some metric spaces using CNs of BFSs. In this research paper, we extend VIKOR method in the context of CNs based metrics, which are obtained form bipolar fuzzy numbers (BFNs). Firstly, we develop CNs of BFNs as well as metric spaces based on CNs. We also discuss some interesting properties of proposed metric spaces. Secondly, we develop VIKOR method using CNs based metrics to handle an MAGDM problem under bipolar fuzzy type information. The predominance of proposed metric spaces is also studied by the means of examples. Furthermore, we demonstrate the efficiency of the extended VIKOR method by solving a numerical example, sensitivity analysis and a detailed comparison with some existing approaches.