A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty

TL;DR

This paper critiques existing distance-based ranking methods for intuitionistic fuzzy sets, proves their limitations with nonlinear distances, and proposes a hypervolume-based ranking approach extended to a new multicriteria decision making method, HVAS.

Contribution

It introduces a novel hypervolume based ranking method for intuitionistic fuzzy sets and extends it to a multicriteria decision making framework, addressing nonlinear distance issues.

Findings

Hypervolume ranking outperforms traditional distance methods in certain scenarios.

HVAS provides more reliable rankings for energy alternatives in Turkey.

The proposed method shows competitive results compared to TOPSIS, VIKOR, and CODAS.

Abstract

Ranking intuitionistic fuzzy sets with distance based ranking methods requires to calculate the distance between intuitionistic fuzzy set and a reference point which is known to have either maximum (positive ideal solution) or minimum (negative ideal solution) value. These group of approaches assume that as the distance of an intuitionistic fuzzy set to the reference point is decreases, the similarity of intuitionistic fuzzy set with that point increases. This is a misconception because an intuitionistic fuzzy set which has the shortest distance to positive ideal solution does not have to be the furthest from negative ideal solution for all circumstances when the distance function is nonlinear. This paper gives a mathematical proof of why this assumption is not valid for any of the non-linear distance functions and suggests a hypervolume based ranking approach as an alternative to distance based ranking. In addition, the suggested ranking approach is extended as a new multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS is applied for multicriteria assessment of Turkey's energy alternatives. Results are compared with three well known distance based multicriteria decision making methods (TOPSIS, VIKOR, and CODAS).