Fuzzy tolerance quotient spaces and fuzzy subsets  

作　　者：ZHANG Ling ZHANG Bo 

机构地区：[1]Computer Science&Technology College,Anhui University,Anhui 230039,China [2]State Key Laboratory of Intelligent Technology and Systems,Beijing 100084,China [3]Tsinghua National Laboratory of Information Science&Technology,Beijing 100084,China [4]Information Science&Technology College,Computer Science&Technology Department,Tsinghua University,Beijing 100084,China

出　　处：《Science China(Information Sciences)》2010年第4期704-714,共11页中国科学(信息科学)(英文版)

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)

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.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.

关 键 词：Fuzzy tolerance relation quotient space ISOMORPHISM fuzzy subset 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]