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

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