Toward a Generalization of Rough Sets Based on Active and Passive Relations
Masashi Emoto*, Rolly Intan**, and Masao Mukaidono*
*Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki, Japan
**Department of Informatics Engineering, Petra Christian University, Jl. Siwalankerto 121-131, Surabaya 60236, Indonesia
In the generalization of rough sets, many concepts use a relation weaker than the equivalence relation usually used in classical rough sets, e.g., induced by a conditional probability relation. The conditional probability relation is binary and assumes that the relationship between two data (elements or objects) resembles a relationship between two events in conditional probability. We use the asymmetric property of the conditional probability relation to propose active and passive relations, then discuss a generalization and properties of rough sets based on active and passive relations.
-  D. Dubois and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Academic Press, New York, 1980.
-  D. Dubois and H. Prade, “Rough Fuzzy Sets and Fuzzy Rough Sets,” Intern. J. of General Systems, Vol.17(2-3), pp. 191-209, 1990.
-  R. Intan and M. Mukaidono, “Generalized Fuzzy Rough Sets By Conditional Probability Relations,” International Journal of Pattern Recognition and Artificial Intelligence, Vol.16(7),World Scientific, pp. 865-881, 2002.
-  R. Intan and M. Mukaidono, “Conditional Probability Relations in Fuzzy Relational Database,” Proceedings of RSCTC’00, LNAI 2005, Springer-Verlag, pp. 251-260, 2000.
-  R. Intan, M. Mukaidono, and Y. Y. Yao, “Generalization of Rough Sets with α-coverings of the Universe Induced by Conditional Probability Relations,” Proceedings of RSTGC-2001, pp. 173-176, 2001.
-  G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic: Theory and Applications,” Prentice Hall, New Jersey, 1995.
-  J. Komorowski, A. Pawlak, L. Polkowski, and A. Skowron, “Rough Sets: A Tutorial,” in: S. K. Pal and A. Skowron (Eds.), Rough Fuzzy Hybridization, Springer, pp. 3-98, 1999.
-  Z. Pawlak, “Rough Sets,” International Journal Computation Information Science 11, pp. 341-356, 1982.
-  R. Slowinski and D. Vanderpooten, “A Generalized Definition of Rough Approximations Based on Similarity,” IEEE Transactions on Knowledge and Data Engineering, Vol.12, No.2, pp. 331-336, 2000.
-  A. Tversky, “Features of Similarity,” Psychological Rev. 84(4), pp. 327-353, 1977.
-  Y. Yamaguchi, R. Intan, M. Emoto, and M. Mukaidono, “Generalization of Rough Sets Using Active and Passive Relations,” Proceeding of Intech 2003, pp. 539-544, 2003.
-  L. A. Zadeh, “Similarity Relations and Fuzzy Orderings,” Inform. Sci. 3(2), pp. 177-200, 1970.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.