Rough sets and topological spaces based on similarity

Ordinary topology now has been used in many sub-fields of artificial intelligence, such as knowledge representation, spatial reasoning etc. In this paper, we discuss the relationships between the theory of rough sets and topological spaces. We obtain the concepts of rough sets from topology, also we obtain the concepts of topological space from rough sets. Furthermore, if the function between two topological spaces is bijective, open and continuous, then the image and the inverse image of a rough set are also rough. © 2012 Springer-Verlag.