Entropy is used to measure the uncertain degree of fuzzy sets and has been widely used in
many fields. This paper introduces an axiomatic definition of entropy measure and a novel …

This contribution reviews critically the existing entropy measures for probabilistic hesitant
fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively …

Hesitant fuzzy set (HFS) is a powerful decision tool to express uncertain information more
flexibly and comprehensively. The aim of this paper is to propose more reasonable …

Hesitant fuzzy sets (HFSs) are beneficial tools for expressing the hesitancy of decision
makers (DMs) to access alternatives in daily life, thereby enabling the membership of an …

In this paper, we first review the existing entropy measures for hesitant fuzzy elements
(HFEs) and demonstrate that the existing entropy measures for HFEs fail to effectively …

In this paper, new entropy measures for hesitant fuzzy sets (HFSs) are proposed. Measuring
uncertainty for an HFS is computed by an amount of distinction between an HFS and its …

We introduce the concepts of entropy and cross‐entropy for hesitant fuzzy information, and
discuss their desirable properties. Several measure formulas are further developed, and the …

In recent years, the concept of probabilistic hesitant fuzzy sets (P-HFSs) has been proposed
as an improvement of hesitant fuzzy sets (HFSs), which has the advantage of representing …

The probabilistic hesitant fuzzy sets (PHFSs), which have received a lot of attention and
have been widely used in many domains, are effective in describing hesitant evaluations …

Probabilistic hesitant fuzzy sets (PHFSs)(Zhu in Decision method for research and
application based on preference relation, 2014.; Xu and Zhou in Fuzzy Optim Decis Making …