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

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. Eventually, the proposed PHFE entropy measures and PHFE entropy‐based distance measures are applied to decision making in the strategy initiatives where their reliability and effectiveness are verified.

A Single‐Valued Extended Hesitant Fuzzy Score‐Based Technique for Probabilistic Hesitant Fuzzy Multiple Criteria Decision‐Making

“…Ranking of alternatives and the best one 10 Complexity including Zhang et al [21] and Farhadinia and Herrera-Viedma [23]. e problem here is that we are seeking the best Chinese hospital with regards to the medical resource restriction and the old-age limitation of target population.…”

“…In a completely updated study, Farhadinia [20] pointed out that there exist two kinds of normalization processes in dealing with PHFS decision-making problems, namely, the probabilistic normalization and cardinal normalization. We need to mention that, among the contributions considering different types of probabilistic-unification processes, the most eminent works are those of Zhang et al [21], Farhadinia and Xu [22], Farhadinia and Herrera-Viedma [23], Li and Wang [24], Wu et al [25], and Lin et al [26]. Except Lin et al's [26] probabilistic-unification process, Farhadinia [20] demonstrated that the other probabilistic-unification processes considered in the later-mentioned contributions are not reasonable from a mathematical point of view.…”

An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information

“…Garg and Kaur [29] also extended Maclaurin mean operator to PDHFS for gesture understanding in brain hemorrhage situations. Farhadinia et al [30] proposed new correlation measures along with its theoretical base and evaluated strategies. Liu et al [31] developed an integrated approach with PHFI using entropy measure and regret theory for venture capital investment assessment.…”

“…Li et al [32] put forward an ORESTE-based approach with PHFI by making use of new distance measure for choosing apt research topic. Farhadinia and Herrera-Viedma [33] fine-tuned the PHFI and developed theoretical base for the same by introducing operational laws and evaluating safety of industries in automobile sector. Li et al [34] made a consensus model with PHFI by introducing normalized PHFI for candidate selection and evaluation.…”

A measure of probabilistic hesitant I‐fuzzy sets and decision makings for strategy choice

“…The most common measure methods are distance measures, similarity measures, and entropy measures. [30][31][32] Farhadinia et al 33 developed 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. However, these measures exist a lot of tedious calculation work, and their application always are limited in some simple comparisons and MADM.…”