In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semant...In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.展开更多
1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of opera...1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex展开更多
Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some m...Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C＊ （E） X（aw） G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T展开更多
文摘In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.
文摘1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex
基金Supported by National Natural Science Foundation of China （Grant Nos. 10771161, 11071188）
文摘Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C＊ （E） X（aw） G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T
