[1]ZHENG Tingting,SANG Xiaoshuang,MA Binbin.α-cut sets of hesitant fuzzy sets and their applications[J].CAAI Transactions on Intelligent Systems,2017,12(3):362-370.[doi:10.11992/tis.201704026]
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α-cut sets of hesitant fuzzy sets and their applications

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 12 Number of periods: 2017 3 Page number: 362-370 Column: 学术论文—智能系统 Public date: 2017-06-25
Title:
α-cut sets of hesitant fuzzy sets and their applications
Author(s):
ZHENG Tingting;  SANG Xiaoshuang;  MA Binbin
School of Mathematical Sciences, Anhui University, Hefei 230601, China
Keywords:
hesitant fuzzy set; type-1 fuzzy set; interval type-2 fuzzy set; α-cut set; decomposition theorem; extension principle; multiple attribute decision-making; clustering analysis
CLC:
TP18;O159
DOI:
10.11992/tis.201704026
Abstract:
The typical cut set is a bridge between fuzzy sets and clarity sets. The hesitant fuzzy set (HFS) theory, as an extension of the classical fuzzy set theory, has not been thoroughly studied till date; furthermore, there is less discussion regarding the relation between the HFS and classical type-I fuzzy set theory or other fuzzy set theories. This study analyzed the relations between the HFS and type-1 fuzzy set theory and between HFS and interval type-2 fuzzy set theory, proposed the concept of α-cut sets of HFS, and discussed their properties. Meanwhile, the decomposition (representation) theorems and the more general extension principles of HFS based on α-cut sets were deduced. The corresponding properties were studied. The results of the simulation prove the rationality of the α-cut set concept and provide a novel method for hesitant fuzzy multiple attribute decision-making and clustering analysis. All these conclusions deeply enrich the fundamental theory of HFS.
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