Belief and plausibility measures on pythagorean fuzzy sets and its applications with BPI-VIKOR

Abstract

Fuzzy sets (FSs) with belief and plausibility measures in Dempster-Shafer theory (DST) are recognized as different methodology to model imperfect, uncertain, and vague information more accurately than probability. Various generalizations of DST to FSs are suggested in the numerous literatures but the generalization of DST to Pythagorean fuzzy sets (PFSs) has not yet been considered so far. In this paper, we first suggest an intuitive and simple way to develop a generalization of DST to PFSs with the characterization of belief function in terms of membership function and plausibility function in terms of 1-nonmemberhip function respectively. We give the interpretation of belief and plausibility on PFSs and then construct belief-plausibility intervals (BPIs) of PFSs. On the basis of suggested BPIs, we use Hausdorff distance to describe the distance between two BPIs and then construct several similarity measures in the generalized context of DST to PFSs. By utilizing the method of VIekriterijumsko KOmpromisno Rangiranje (VIKOR), the suggested belief and plausibility measures on PFSs in the framework of DST enable us to develop a belief-plausibility VIKOR (BP-VIKOR) to manage multicriteria decision-making (MCDM) problems related to daily life settings. Numerical analysis with examples are given to show the suggested method is reasonable, and suitable in the environment of PFSs in the context of generalization of DST.