基于对象的广义粗糙近似算子的拓扑性质  

Topological Properties of Generalized Rough Approximation Operators Based on Objects

作　　者：李妍妍 秦克云[1] LI Yanyan;QIN Keyun(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》2023年第2期173-177,共5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。近似算子是粗糙集理论中的核心概念,基于等价关系的Pawlak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。文中主要研究基于对象的广义粗糙近似算子诱导拓扑的性质,证明了广义近似空间中所有可定义集形成拓扑的充分条件也是其必要条件,研究了该拓扑的正则、正规性等拓扑性质;给出了串行二元关系与其传递闭包可以生成相同拓扑的等价条件;讨论了该拓扑与任意二元关系下基于对象的广义粗糙近似算子所诱导拓扑之间的相互关系。Rough set theory is a mathematical tool to deal with uncertain problems.The core notion of rough set theory is appro-ximation operators.Pawlak approximation operators based on equivalence relations cab be 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 object-based generalized rough approximation operators.It is proved that the sufficient condition for all definable subsets in a generalized approximation space to form a topology is also its necessary condition.The regularity and normality of this topology are studied.The equivalent conditions for the same topology generated by the serial binary relation and its transitive closure are given.The relationship between this topology and the topology induced by the object-based generalized rough approximation operator under any binary relation is discussed.

关 键 词：串行二元关系 基于对象的广义粗糙近似算子 拓扑 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]