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

查看全文 作　　者：YUAN XueHai LI HongXing SUN [1]KaiBiao

机构地区：[1]School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China

出　　处：《Science China(Information Sciences)》索引2011年第54卷第1期,共20页

基　　金：supported by the Major Research Plan of the National Natural Science Foundation of China(Grant No.90818025) 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. 关键词：区间值模糊集直觉模糊集分解定理表现定理割集表示定理截集定义

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

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