The Connectivity of the Covering Approximation Space
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.
KeywordsCovering approximation space Connectivity Granular computing
This work is in part supported by The National Nature Science Foundation of China under Grant Nos. 61170128, 61379049 and 61379089, the Key Project of Education Department of Fujian Province under Grant No. JA13192, the Project of Education Department of Fujian Province under Grant No. JA14194, the Zhangzhou Municipal Natural Science Foundation under Grant No. ZZ2013J03, and the Science and Technology Key Project of Fujian Province, China Grant No. 2012H0043.
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