Generalization of Rough Sets with α-Coverings of the Universe Induced by Conditional Probability Relations
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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
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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