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.
Keywords
References
Bollobás, B.: Modern Graph Theory. Springer, New York (1998)
Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Extensions and intentions in the rough set theory. Inf. Sci. 107, 149–167 (1998)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)
Gao, S.: Graph Theory and Network Flow Theory. Higher Education Press, Beijing (2009)
Ge, X.: Connectivity of covering approximation spaces and its applications on epidemiological issue. Appl. Soft. Comput. 25, 445–451 (2014)
Jensen, R., Shen, Q.: Finding rough set reducts with ant colony optimization. In: Proceedings of the 2003 UK Workshop on Computational Intelligence, pp. 15–22 (2003)
Lai, H.: Matroid Theory. Higher Education Press, Beijing (2001)
Lin, T.Y.: Granular computing on binary relations. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 296–299. Springer, Heidelberg (2002)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3–27 (2007)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Wang, F.: Outline of a computational theory for linguistic dynamic systems: toward computing with words. Int. J. Intell. Control Syst. 2, 211–224 (1998)
Wang, Z., Shu, L., Ding, X.: Minimal description and maximal description in covering-based rough sets. Fundamenta Informaticae 128, 503–526 (2013)
Wang, S., Zhu, W., Zhu, Q., Min, F.: Characteristic matrix of covering and its application to boolean matrix decomposition. Inf. Sci. 263, 186–197 (2014)
Wang, S., Zhu, W., Zhu, Q., Min, F.: Four matroidal structures of covering and their relationships with rough sets. Int. J. Approximate Reasoning 54, 1361–1372 (2013)
West, D., et al.: Introduction to Graph Theory. Pearson Education, Singapore (2002)
Wu, W., Leung, Y., Mi, J.: On characterizations of (I, T) -fuzzy rough approximation operators. Fuzzy Sets Syst. 154, 76–102 (2005)
Yao, Y.Y.: On generalizing pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, p. 298. Springer, Heidelberg (1998)
Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111, 239–259 (1998)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zakowski, W.: Approximations in the space (u, \(\pi \)). Demonstratio Mathematica 16, 761–769 (1983)
Zhu, W., Wang, F.: Reduction and axiomization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)
Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)
Zhu, W., Wang, F.: On three types of covering-based rough sets. IEEE Trans. Knowl. Data Eng. 19, 1131–1144 (2007)
Zhu, W., Wang, F.: A new type of covering rough sets. In: 2006 3rd International IEEE Conference on Intelligent Systems, pp. 444–449. IEEE (2006)
Acknowledgments
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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Ma, D., Zhu, W. (2015). The Connectivity of the Covering Approximation Space. In: Ciucci, D., Wang, G., Mitra, S., Wu, WZ. (eds) Rough Sets and Knowledge Technology. RSKT 2015. Lecture Notes in Computer Science(), vol 9436. Springer, Cham. https://doi.org/10.1007/978-3-319-25754-9_38
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