完备的完全分配格上粗糙集的拓扑性质  

The Topological Properties of the Rough Set on a Complete Completely Distributive Lattice

作　　者：周宁琳[1,2] 胡宝清 ZHOU Ning-lin;HU Bao-qing(School o{ Science,Hubei University o{ Technology,Wuhan 430068,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]湖北工业大学理学院,湖北武汉市430068 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《模糊系统与数学》2018年第4期174-179,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11571010;61179038);湖北工业大学博士启动基金资助项目(BSQD14065)

摘　　要：本文讨论了定义在完备的完全分配格L上的粗糙集模型的拓扑结构。此粗糙集模型是现有的一些粗糙集模型和模糊粗糙集模型的统一形式。通过在格上讨论其拓扑性质,我们得到在一定条件下,此粗糙集的所有上近似集和下近似集分别构成L的一个闭拓扑。并且当此粗糙集的二元关系是序等价关系时,这两个闭拓扑是相同的。In this paper we discuss the topological properties of the rough set on a complete completely distributive lattice, which is a united framework of some rough set models and rough fuzzy set models. We conclude that the set of all lower rough approximation of this rough set and the set of all upper rough approximation of this rough set construct two topological molecular lattices, respectively. When the relation that the rough set based on is an order equivalence relation, these two topological molecular lattices are the same.

关 键 词：粗糙集 拓扑分子格 完备的完全分配格 二元关系 

分 类 号：O159[理学—数学]