粗糙群和基于子群的群的粗糙  

Rough Group and the Roughness of Group Based on Subgroup

作　　者：张贤勇[1] 莫智文[1] 

机构地区：[1]四川师范大学基础部

出　　处：《四川师范大学学报（自然科学版）》2006年第3期253-256,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(69803007);四川省青年科学基金资助项目

摘　　要：运用粗糙集理论的思想,在群中基于子群定义了群的近似空间,并定义了集合的运算,用集合的近似进行了研究.用近似群重新定义了粗糙群理论中的粗糙群、粗糙子群、粗糙不变子群、粗糙商群、粗糙同态、粗糙同构等一系列概念,并在传统的和新定义的两种粗糙群理论体系中,研究了基于子群的群的粗糙的性质.In this Paper, in terms of the rough set theory the concept of approximate space of group is defined based on a subgroup. Operations of sets are defined and studied by set approximation. The notions in rough group theory are redefined by approximate groups, such as rough group, rough subgroup, rough invariant subgroup, rough quotient group, rough homomorphism, rough isomorphism, etc. In both systems of traditional rough group theory and redefined one, the properties of roughness of group based on subgroup are studied.

关 键 词：粗糙集 群 粗糙群 近似群 粗糙同态 

分 类 号：O159[理学—数学] TP18[理学—基础数学]