Generalized rough sets based on neighborhood systems and topological spaces

Rough sets theory is an important method for dealing with uncertainty, fuzziness and undefined objects. In this paper, we introduce a new approach for generalized rough sets based on the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approximation operators are generated from the core of neighborhood systems. Relationship among different approximation operators are presented. We generate different topological spaces by using the core of these neighborhood systems. Relationship among different generated topologies are discussed.