[1]郑婷婷,桑小双,马斌斌.犹豫模糊集的α-截集及其应用[J].智能系统学报,2017,12(03):362-370.[doi:10.11992/tis.201704026]
 ZHENG Tingting,SANG Xiaoshuang,MA Binbin.α-cut sets of hesitant fuzzy sets and their applications[J].CAAI Transactions on Intelligent Systems,2017,12(03):362-370.[doi:10.11992/tis.201704026]
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犹豫模糊集的α-截集及其应用(/HTML)
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《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第12卷
期数:
2017年03期
页码:
362-370
栏目:
出版日期:
2017-06-25

文章信息/Info

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 settype-1 fuzzy setinterval type-2 fuzzy setα-cut setdecomposition theoremextension principlemultiple attribute decision-makingclustering 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.

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备注/Memo

备注/Memo:
收稿日期:2017-04-20。
基金项目: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).
作者简介:郑婷婷,女,1978年生,副教授,博士,主要研究方向为粗糙集、模糊集和粒计算理论。主持安徽省自然科学基金1项,安徽省教育厅高校优秀青年人才项目1项,近年来发表学术论文20余篇;桑小双,女,1990年生,硕士研究生,主要研究方向为模糊集、机器学习;马斌斌,男,1992年生,硕士研究生,主要研究方向为粗糙集、机器学习。
通讯作者:郑婷婷.E-mail:tt-zheng@163.com.
更新日期/Last Update: 2017-06-25