Topological Properties of a Pair of Relation-Based Approximation Operators

Abstract

Rough set theory is an important tool to data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and has been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separate property and Lindelof property of the topological space are discussed. The result is not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to the theory of topology.