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Similarity and entropy measures for hesitant fuzzy sets
Author(s) -
Hu Junhua,
Yang Yan,
Zhang Xiaolong,
Chen Xiaohong
Publication year - 2018
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12477
Subject(s) - entropy (arrow of time) , upper and lower bounds , fuzzy set , fuzzy logic , hfss , mathematics , similarity (geometry) , mathematical optimization , data mining , computer science , fuzzy number , artificial intelligence , mathematical analysis , telecommunications , physics , microstrip antenna , quantum mechanics , antenna (radio) , image (mathematics)
Hesitant fuzzy sets (HFSs) are beneficial tools for expressing the hesitancy of decision makers (DMs) to access alternatives in daily life, thereby enabling the membership of an element to a set that is represented by several possible values. This study proposes an interval bound footprint (IBF), which describes the fluctuation range of the values of hesitant fuzzy elements (HFEs) arranged in order. In addition, a few similarity and entropy measures for HFSs are deduced. First, the interval bound footprint, upper bound footprint, and lower bound footprint for HFEs are defined and their corresponding properties are discussed. Subsequently, several similarity and entropy measures for HFSs are presented based on IBF. Lastly, a hesitant fuzzy multi‐criteria decision‐making method based on the proposed similarity and entropy measures is introduced. We use a numerical example to discuss the differences among the proposed similarity measures and the applicable environment based on the risk preferences of the different DMs.