Topological characterizations for three covering approximation operators

Abstract

The topological properties of coverings and their corresponding covering approximation operators have drawn special attention because these topological properties have important applications in rough sets. In this paper, we present some topological characterizations for three covering approximation operators. In the first part, we present certain topological characterizations for the covering lower approximation operator in an infinite universe, while the topological characterizations for the first and the second types of covering upper approximation operators are studied in a finite universe. In the second part, the relationships among three operators and the relationships among three topological spaces are established. In a word, topology theory provides useful tools to study covering-based rough sets. © 2013 Springer-Verlag.