An Extension of TODIM with VIKOR approach based on Gini Simpson Index of Diversity under Picture fuzzy framework to Evaluate Opinion Polls

Abstract

Cuong and Kreinovich was the first who gives the idea of Picture fuzzy set (PFS), which is an extension of intuitionistic fuzzy set (IFS) by cosidering positive, negative and neutral membership of element. In this paper, we have been worked on new entropy measure of PFS from the probabilistic view point and it’s properties are examined from mathematical point of view. A hybrid aproach is presented with the assistance of TODIM (Portuguese abbreviation for Interactive Multi-Criteria Decision Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) methods. Further, we applied it to MCDM (multi criterion decision making) problems with picture fuzzy numbers (PFNs), where the information about criteria synthetic weights is partially known and completely unknown and show its existence with the help of some practical cases. After getting the output, we are able to infer that the proposed hybrid approach is comparatively better so as to handle the uncertainty and vulnerabilities for the decision making problems. Based upon these two approaches we can determine the opinion poll of voting outcomes and then, we compare its result with other MCDM approaches that exists in the literature.