Uncertainty Measures for Hesitant Fuzzy Information

Na Zhao · Zeshui Xu · Fengjun Liu

40 citations0/0 files storedInternational Journal of Intelligent Systems

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Multi-Criteria Decision Making Fuzzy and Soft Set Theory Fuzzy Systems and Optimization

Abstract

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.

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References

1965Fuzzy sets 1996Fuzzy sets 1986Intuitionistic fuzzy sets 1980Fuzzy Sets and Systems - Theory and Applications 2010Hesitant fuzzy sets 1972A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory 2010Hesitant fuzzy information aggregation in decision making 2009On hesitant fuzzy sets and decision

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