Topological Properties of Generalized Rough Approximation Operators Based on Objects

Abstract

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.

Keywords

• serial binary relation|object-based generalized rough approximation operator|topology