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

Sunit Kumar Et.Al

doi:10.17762/turcomat.v12i3.1654

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.

Highlights

Zadeh (1965) was the one who developed the basic idea of Fuzzy set (FS) which plays a significant role in decision making under uncertainty which contains only a membership degree
The main motive of this paper is to combine the concept of TODIM and VIKOR approaches to tackle with the MCDM problems with picture fuzzy numbers (PFNs)
To contribute a new PF information measure which is based on Gini Simpson entropy, (c) To introduce an extended PF-TODIM-VIKOR method under picture fuzzy framework, which fully takes the advantags of entropy information, prospect theory and compromise solution, (d) A numerical example of election outcomes is described to verify the practical applicibility of the developed algorithm, (e) A deatiled comparative study and discussion are put forward to illustarte the superiority and effectiveness of the developed algorithm

Summary

Introduction

Zadeh (1965) was the one who developed the basic idea of Fuzzy set (FS) which plays a significant role in decision making under uncertainty which contains only a membership degree. We found the concept of neutral degree in various situations when we go through the human opinion like: sure, refrain, no, denial The main motive of this paper is to combine the concept of TODIM and VIKOR approaches to tackle with the MCDM problems with PFNs. The main contribution are : (a).To introduce a new criteria for PF-entropy, (b). To contribute a new PF information measure which is based on Gini Simpson entropy, (c) To introduce an extended PF-TODIM-VIKOR method under picture fuzzy framework, which fully takes the advantags of entropy information, prospect theory and compromise solution, (d) A numerical example of election outcomes is described to verify the practical applicibility of the developed algorithm, (e) A deatiled comparative study and discussion are put forward to illustarte the superiority and effectiveness of the developed algorithm.

Preliminaries

Background

Proposed PF Information Measure

Approch 2

Methods

Conclusions