Uncertainty measures for probabilistic hesitant fuzzy sets in multiple criteria decision making

TL;DR

This paper reviews existing entropy measures for probabilistic hesitant fuzzy sets, identifies their limitations, and proposes a new axiomatic framework with flexible entropy formulas and distance measures for improved uncertainty quantification in decision making.

Contribution

It introduces a novel axiomatic framework for entropy measures of probabilistic hesitant fuzzy elements, addressing limitations of previous measures and enabling better uncertainty assessment.

Findings

Existing entropy measures often fail to distinguish different PHFSs effectively.

New entropy formulas are derived considering fuzziness and nonspecificity.

Entropy-based distance measures are proposed for comparative analysis.

Abstract

This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In the sequel, we develop a new axiomatic framework of entropy measures for probabilistic hesitant fuzzy elements (PHFEs) by considering two facets of uncertainty associated with PHFEs which are known as fuzziness and nonspecificity. Respect to each kind of uncertainty, a number of formulae are derived to permit flexible selection of PHFE entropy measures. Moreover, based on the proposed PHFE entropy measures, we introduce some entropy-based distance measures which are used in the portion of comparative analysis.