The cut sets, decomposition theorems and representation theorems on intuitionistic fuzzy sets and interval valued fuzzy sets

被引：32

作者：

Yuan XueHai ^{[1
]}

Li HongXing ^{[1
]}

Sun KaiBiao ^{[1
]}

机构：

[1] Dalian Univ Technol, Sch Elect & Informat Engn, Dalian 116024, Peoples R China

来源：

SCIENCE CHINA-INFORMATION SCIENCES | 2011年 / 54卷 / 01期

基金：

中国国家自然科学基金;

关键词：

intuitionistic fuzzy sets; interval valued fuzzy sets; triple valued fuzzy sets; cut sets; decomposition theorem; representation theorem;

D O I：

10.1007/s11432-010-4078-6

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, the cut sets, decomposition theorems and representation theorems of intuitionistic fuzzy sets and interval valued fuzzy sets are researched indail. First, new definitions of four kinds of cut sets on intuitionistic fuzzy sets are introduced, which are generalizations of cut sets on Zadeh fuzzy sets and have the same properties as that of Zadeh fuzzy sets. Second, based on these new cut sets, the decomposition theorems and representation theorems on intuitionistic fuzzy sets are established. Each kind of cut sets corresponds to two kinds of decomposition theorems and representation theorems. Thus eight kinds of decomposition theorems and representation theorems on intuitionistic fuzzy sets are obtained, respectively. At last, new definitions of cut sets on interval valued fuzzy sets are given based on the theory of cut sets on intuitionistic fuzzy sets, and eight kinds of decomposition theorems and representation theorems on interval valued fuzzy sets are also obtained. These results provide a fundamental theory for the research of intuitionistic fuzzy sets and interval valued fuzzy sets.

引用

页码：91 / 110

页数：20

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