Abstract
Standard rough set theory is developed based on the notion of indiscernibility of elements of a universe. Typically, indiscernibility is modeled by an equivalence relation, which may not provide a realistic description of real-world relationships between elements. In this paper, the notion of weak fuzzy similarity relations, a generalization of fuzzy similarity relations, is used to represent indiscernibility of elements. A specific type of weak fuzzy similarity relations, called conditional probability relations, is discussed. Generalized rough set approximations are defined by using a-coverings of the universe induced by a weak fuzzy similarity relation. Three types of rough membership functions are defined and their properties are examined.
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Intan, R., Yao, Y.Y., Mukaidono, M. (2003). Generalization of Rough Sets Using Weak Fuzzy Similarity Relations. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36473-3_4
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DOI: https://doi.org/10.1007/978-3-540-36473-3_4
Publisher Name: Springer, Berlin, Heidelberg
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