The connectivity of the covering approximation space

Abstract

As a covering approximation space, its connectivity directly reflects a relationship, which plays an important role in data mining, among elements on the universe. In this paper, we study the connectivity of a covering approximation space and give its connected component. Especially, we give three methods to judge whether a covering approximation space is connected or not. Firstly, the conception of the maximization of a family of sets is given. Particularly, we find that a covering and its maximization have the same connectivity. Second, we investigate the connectivity of special covering approximation spaces. Finally, we give three methods of judging the connectivity of a covering approximation space from the viewpoint of matrix, graph and a new covering.