In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. The...In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.展开更多
Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques...Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras.展开更多
基金Natural Science Foundation of Jiangsu Province of China ( No.BK2006176)High-Tech Key Laboratory of Jiangsu,China (No.BM2007201)
文摘In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.
基金supported by National Natural Science Foundation of China (Grant No.11001078)Shanghai Municipal Education Commission and Shanghai Education Development Foundation (GrantNo. 11CG30)
文摘Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras.
