Abstract
Rough set theory is developed based on the notion of equivalence relation, but the property of equivalence has limited its application fields, which may not provide a realistic description of real-world relationships between elements. The paper presents a transition from the equivalence relation to the compatibility relation, called Compatibility Rough Set Theory or, in short, CRST. A specific type of fuzzy compatibility relations, called conditional probability relations, is discussed. All basic concepts or rough set theory are extended. Generalized rough set approximations are defined by using coverings of the universe induced by a fuzzy compatibility relation. Generalized rough membership functions are defined and their properties are examined.
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Hong, T., Pixi, Z., Xiukun, W. (2005). CRST: A Generalization of Rough Set Theory. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_38
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DOI: https://doi.org/10.1007/11548669_38
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