群中模糊集的上近似集合与下近似集合  

The Upper and Lower Approximations of Fuzzy Sets in a Group

作　　者：王莉[1] 毕全起[2] 

机构地区：[1]锦州师范学院数学系,辽宁锦州121003 [2]河北师范大学数学与信息科学学院,河北石家庄050016

出　　处：《河北师范大学学报（自然科学版）》2001年第4期450-452,共3页Journal of Hebei Normal University：Natural Science

基　　金：辽宁省教育厅攀登计划资助项目 ( 2 0 16 10 49)

摘　　要：粗糙集概念是由 Pawlak于 1 982年提出的 ,现已从许多方面作了推广 .粗糙集与模糊集的结合近年来越来越受到国际学术界的关注 .现在研究群中模糊集的上、下近似 ,并且讨论了近似算子的乘积结构 ,定义了粗糙模糊子群的概念 ,证明了群的模糊子群一定是粗糙模糊子群 .在同态映射下 ,子群的像的上下近似也一定是它的上。The theory of rough set is proposed by Z.Pawlak in 1982.It is extended from various points of sides.The combination of rough set and fuzzy set is studied by many authors.The concepts of upper and lower approximations of fuzzy sets in a group are given,and the product structure of approximation operators is studied.The concept of rough fuzzy subgroup is also definde.It is proved that a fuzzy subgroup of a group is a rough fuzzy subgroup.Under a homostasis mapping,the upper and lower approximations of the images of a subgroup are just the images of their apper and lower approximations.

关 键 词：粗糙模糊子群 上近似集合 下近似集合 粗糙集 模糊集 同态像 群 

分 类 号：O152[理学—数学] O159[理学—基础数学]