粗糙线性近似空间的代数结构  

The algebraic structure of rough linear approximation space

作　　者：刘亚梅[1] 马盈仓[1] 鲁文霞[1] 陈艳艳[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《智能系统学报》2014年第2期224-228,共5页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(60775038);陕西省教育厅专项科研计划资助项目(12JK0878)

摘　　要：针对线性空间上引入上下近似算子后的代数结构的刻画问题,根据基于同余关系的线性空间上下近似的性质,提出2个新的集合,分别对上近似的并和下近似的交的包含关系进行了改进,得出了集合交的上近似、集合并的下近似的等式刻画。进而,定义引入粗糙线性近似空间的概念,并在其上引入交、并、补的运算,得出粗糙线性近似空间在运算下构成了布尔代数的结论,丰富了线性空间与粗糙集理论相结合的研究。Focusing on the description of the algebraic structure on the upper （lower） approximation, and according to the properties of the upper （lower） approximation in rough linear space, two new sets are presented, and the in- clusion relation of the upper approximation＇ s union and the lower approximation＇s intersection are improved, deri- ving the equation expressions of the upper approximation＇ s union and the lower approximation＇s intersection. More- over, the rough linear approximation space is proposed and the intersection, union and complementary operations are introduced in the rough linear approximation space. Finally, it has been proven that the rough linear approxima- tion space is Boolean algebra on the intersection, union and complementary operations. This paper enriches the combination of linear space and rough set research.

关 键 词：粗糙线性近似空间 线性子空间 同余 上下近似 布尔代数 代数结构 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] B815[自动化与计算机技术—控制科学与工程]