Axiomatic framework of fuzzy entropy and hesitancy entropy in fuzzy environment

Entropy is a vital concept to measure uncertainties, in order to measure the uncertainties of fuzzy sets (FSs), intuitionist fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs) more fully, in this paper, the axiomatic definition of fuzzy entropy of FSs is modified, the entropy measures of IFSs and PFSs are categorized as fuzzy entropy and hesitancy entropy, and the axiomatic definitions of these two entropy measures are also revised. Further, the axiomatic definitions of two overall entropies are given based on fuzzy entropy and hesitancy entropy, and the expressions of overall entropy of IFSs and PFSs are constructed by special functions. Then, it is shown that three existing overall entropy formulas can be constructed by three particular functions, and their rationality is proved. Finally, the effectiveness and feasibility of the proposed method and overall entropy are illustrated by an example and two comparative analyses.