Fuzzy tolerance quotient spaces and fuzzy subsets

作     者：ZHANG Ling1 & ZHANG Bo2,3,4* 1Computer Science & Technology College, Anhui University, Anhui 230039, China 2State Key Laboratory of Intelligent Technology and Systems, Beijing 100084, China 3Tsinghua National Laboratory of Information Science & Technology, Beijing 100084, China 4Information Science & Technology College, Computer Science & Technology Department, Tsinghua University, Beijing 100084, China 

作者机构：Computer Science & Technology College Anhui University Anhui China State Key Laboratory of Intelligent Technology and Systems Beijing China Tsinghua National Laboratory of Information Science & Technology Beijing China Information Science & Technology College Computer Science & Technology Department Tsinghua University Beijing China 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2010年第53卷第4期

页      面：704-714页

核心收录：

学科分类：0810[工学-信息与通信工程] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (Grant No. 60621062) the National Basic Research Program of China (Grant Nos. 2004CB318108, 2007CB311003) 

主　　题：Fuzzy tolerance relation quotient space isomorphism fuzzy subset 

摘      要：The structure and characteristic of fuzzy subsets are discussed by using the concepts of granulation and hierarchy in quotient space theory. First, the equivalence relation based quotient space theory is extended to the fuzzy tolerance relation. Second, the isomorphism and its discriminant of fuzzy tolerance relations are discussed. Finally, by using the fuzzy tolerance relation to define the fuzzy subset, its properties are addressed. The main results are given below: (1) several equivalent statements of fuzzy tolerance relations; (2) the definition of isomorphism of fuzzy tolerance relations; (3) the isomorphic discriminant of fuzzy tolerance relations; (4) the definition and properties of fuzzy subsets based on the fuzzy tolerance relations; and (5) the necessary and sufficient condition of the isomorphism of fuzzy subsets. These results will help us further comprehend the concepts of fuzzy tolerance relations and fuzzy subsets.