Journal
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
Volume 31, Issue 1, Pages 673-685Publisher
IOS PRESS
DOI: 10.3233/IFS-2180
Keywords
Hesitant fuzzy set; entropy measure; multi-criteria decision-making
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Funding
- National Natural Science Foundation of China [71371107]
- National Science Foundation of Shandong Province [ZR2013GM011]
- Spanish National research project [TIN2015-66524-P]
- Spanish Ministry of Economy and Finance Postdoctoral Training [FPDI-2013-18193]
- ERDF
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Entropy is used to measure the uncertain degree of fuzzy sets and has been widely used in many fields. This paper introduces an axiomatic definition of entropy measure and a novel entropy formula for hesitant fuzzy elements (HFEs). Afterwards, a general form of entropy measures for HFEs is proposed, from which a family of concrete entropy formulas for HFEs can be derived. Compared with the existing ones, these formulas can measure both fuzziness and hesitation of HFEs, as a result, the uncertain information can be described in a more appropriate manner. The proposed axiomatic definition and entropy formulas are used to define the entropy measure for hesitant fuzzy sets. A multi-criteria decision making model which uses the proposed entropy measures for HFEs to compute the criteria weights and obtain a ranking of alternatives is introduced.
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