Uncertainty Measures for Hesitant Fuzzy Information

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 distinguish some apparently different HFEs in some cases. Then, we propose a new axiomatic framework of entropy measures for HFEs by taking fully into account two facets of uncertainty associated with an HFE (i.e., fuzziness and nonspecificity). We adopt a two-tuple entropy model to represent the two types of uncertainty associated with an HFE. Additionally, we discuss how to formulate each kind of uncertainty. For each of fuzziness and nonspecificity, some simple methods are provided to construct measures, which can well handle the problems in the existing entropy measures for HFEs. Several examples are given to illustrate each method, and comparisons with the existing entropy measures are also offered.