广义粗糙近似算子的拓扑性质  

On Topological Properties of Generalized Rough Approximation Operators

作　　者：李妍妍 秦克云[1] LI Yan-yan;QIN Ke-yun(College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《计算机科学》2022年第3期263-268,共6页Computer Science

基　　金：国家自然科学基金(61976130)。

摘　　要：粗糙集理论是一种处理不确定性问题的数学工具。粗糙近似算子是粗糙集理论中的核心概念,基于等价关系的Pawlak粗糙近似算子可以推广为基于一般二元关系的广义粗糙近似算子。近似算子的拓扑结构是粗糙集理论的重点研究方向。文中主要研究基于一般二元关系的广义粗糙近似算子诱导拓扑的性质,给出了基于粒和基于子系统的广义粗糙近似算子诱导的4种拓扑,研究了它们之间的关系;通过对象的右邻域系统给出了基于粒的广义近似算子诱导的拓扑的基,研究了相应拓扑的正规性与正则性;通过分析基于子系统的广义上近似算子的性质,证明了基于子系统的广义上近似算子诱导的拓扑可以转化为基于对象的广义下近似算子诱导的拓扑。Rough set theory is a mathematical tool for dealing with uncertain information.The core notions of rough set theory is approximation operators of approximation spaces.Pawlak approximation operators are established by using equivalence relations on the universe.They are extended to generalized rough approximation operators based on arbitrary binary relations.The topological structures of approximation operators are important topics in rough set theory.This paper is devoted to the study of topological properties of generalized rough approximation operators induced by arbitrary binary relations.Four types of topologies induced by generalized approximation operators based on granules and subsystems are presented and the relationships among these four types of topologies are discussed.The bases of the topologies induced by generalized approximation operators based on granules are presented by the right-neighborhood systems for objects,and the normality and regularity for related topologies are investigated.By analyzing the properties of the generalized upper approximation operators based on the subsystem,it is proved that the topologies induced by the subsystem-based generalized upper approximation operators can be transformed into the topologies induced by the generalized lower approximation operators based on the objects.

关 键 词：粒 子系统 广义粗糙近似算子 拓扑 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]