Entropy measures of multigranular unbalanced hesitant fuzzy linguistic term sets for multiple criteria decision making

The hesitant fuzzy linguistic term set (HFLTS) is an efficient tool for modeling linguistic information in multi-criteria decision making (MCDM), and the entropy measure of HFLTS, as a substantial representation of uncertainty, merits additional investigation. This article aims to exploit a general framework to facilitate the construction of entropy measure for multigranular unbalanced HFLTS. An axiomatic definition of the entropy for HFLTSs that considers both types of uncertainty (fuzziness and hesitation) is presented, with the entropy measure subsequently derived from distance-based mapping. From this definition, several deduced results have been developed for the mapping that depicts the entropy expression in order to get such functions with ease. Whereafter, a MCDM weight-determining model for multigranular unbalanced linguistic information without preset weights is devised, and an empirical application of the suggested model in MCDM is illustrated. Ultimately, comparisons and analyses with existing studies are conducted to demonstrate the advantages of the proposed work.