Hesitant fuzzy information measures and their applications in multi-criteria decision making

Abstract

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 information measures for HFSs in comparison with the existing ones. First, a series of distance measures is suggested for hesitant fuzzy element and hesitant fuzzy sets. These measures are directly calculated from hesitant fuzzy elements without judging the decision-makers’ risk preference and adding any values into the hesitant fuzzy element with the smaller number of elements. Then, some similarity and entropy measures are proposed based on the transforming relationship among the information measures. Additionally, based on the proposed information measures, a TOPSIS method for hesitant fuzzy information is provided. Finally, some numerical examples are used in order to illustrate the proposed decision method and a comparative analysis is made to demonstrate that the suggested measures are more objective and feasible in certain cases.

Keywords:

• hesitant fuzzy sets
• distance measure
• similarity measure
• entropy measure
• multi-criteria decision making

Acknowledgements

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Nature Science Foundation of China [grant number 71371196], [grant number 71431006], [grant number 71221061], [grant number 71210003].