Abstract
Standard rough sets are defined by a partition induced by an equivalence relation representing discernibility of elements. Equivalence relations may not provide a realistic view of relationships between elements in real-world applications. One may use coverings of, or non-equivalence relations on, the universe. In this paper, the notion of weak fuzzy similarity relations, a generalization of fuzzy similarity relations, is used to provide a more realistic description of relationships between elements. A special type of weak fuzzy similarity relations called conditional probability relation is discussed. Generalized rough set approximations are proposed by using α-coverings of the universe induced by conditional probability relations.
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Intan, R. and Mukaidono, M., Conditional probability relations in fuzzy relational database, Proceedings of RSCTC’00, pp. 213–222, 2000.
Intan, R., Mukaidono, M., ‘Fuzzy Functional Dependency and Its Application to Approximate Querying’, Proceedings of IDEAS’00, (2000), pp.47–54.
Klir, G.J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, New Jersey, 1995.
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A., ‘Rough Sets: A Tutorial’, (1999).
Pawlak, Z., Rough sets, International Journal Computation & Information Science, 11, pp. 341–356, 1982.
Polkowski, L. and Skowron, A. (Eds.), Rough Sets in Knowledge Discovery, I, II, Physica-Verlag, Heidelberg, 1998.
Yao, Y.Y., Combination of rough and fuzzy sets based on α-level sets, in: Rough Sets and Data Mining: Analysis for Imprecise Data, Lin, T.Y. and Cercone, N. (Eds.), Kluwer Academic Publishers, Boston, pp. 301–321, 1997.
Yao, Y.Y., A comparative study of fuzzy sets and rough sets, International Journal of Information Science, 109, pp. 227–242, 1998.
Yao, Y.Y. and Zhang, J.P., Interpreting fuzzy membership functions in the theory of rough sets, Proceedings of RSCTC’00, pp. 50–57, 2000.
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Intan, R., Mukaidono, M., Yao, Y.Y. (2001). Generalization of Rough Sets with α-Coverings of the Universe Induced by Conditional Probability Relations. In: Terano, T., Ohsawa, Y., Nishida, T., Namatame, A., Tsumoto, S., Washio, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2001. Lecture Notes in Computer Science(), vol 2253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45548-5_37
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DOI: https://doi.org/10.1007/3-540-45548-5_37
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