Abstract
A fundamental difficulty with fuzzy set theory is the semantical interpretations of membership functions. We address this issue in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. Rough set approximations are related to the core and support of a fuzzy set. A salient feature of the interpretation is that membership values of equivalent or similar elements are related to each other. Two types of similarities are considered, one is defined by a partition of the universe, and the other is denned by a covering.
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© 2001 Springer-Verlag Berlin Heidelberg
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Yao, Y.Y., Zhang, J.P. (2001). Interpreting Fuzzy Membership Functions in the Theory of Rough Sets. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_9
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DOI: https://doi.org/10.1007/3-540-45554-X_9
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