摘要
经典截集是联系模糊集和清晰集的桥梁。犹豫模糊集作为经典模糊集的拓展,它的相关理论研究还不够深入,特别是它与经典Ⅰ型模糊集以及其他模糊集之间的关系还缺少讨论。通过分析犹豫模糊集与Ⅰ型模糊集、区间Ⅱ型模糊集之间的关系,引入了犹豫模糊集的α-截集的概念并讨论其性质,根据该截集推导出犹豫模糊集的分解(表示)定理和更普适的扩展原则。通过分析相关性质及仿真实例,说明了犹豫模糊集的截集概念的合理性,为犹豫模糊多属性决策和聚类分析等问题提供了新的方法。这些结果也极大丰富了犹豫模糊集的相关基础理论。
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 theα-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.
出处
《智能系统学报》
CSCD
北大核心
2017年第3期362-370,共9页
CAAI Transactions on Intelligent Systems
基金
安徽省自然科学基金面上项目(1708085MF163)
安徽省教育厅高校省级优秀青年人才基金重点项目(2013SQRL005ZD)
关键词
犹豫模糊集
Ⅰ型模糊集
区间Ⅱ型模糊集
α-截集
分解定理
扩展原则
多属性决策
聚类分析
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
