犹豫模糊集的α-截集及其应用

PDF下载HTML

Title:

α-cut sets of hesitant fuzzy sets and their applications

作者:

郑婷婷, 桑小双, 马斌斌

安徽大学 数学科学学院, 安徽 合肥 230601

Author(s):

ZHENG Tingting, SANG Xiaoshuang, MA Binbin

School of Mathematical Sciences, Anhui University, Hefei 230601, China

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

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

分类号:

TP18;O159

DOI:

10.11992/tis.201704026

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。

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.