05069600

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05069600 Wu, Wei-Zhi Upper and lower probabilities of fuzzy events induced by a fuzzy set-valued mapping. \'Sl\c ezak, Dominik (ed.) et al., Rough sets, fuzzy sets, data mining, and granular computing. 10th international conference, RSFDGrC 2005, Regina, Canada, August 31 -- September 3, 2005. Proceedings, Part I. Berlin: Springer (ISBN 3-540-28653-5/pbk). Lecture Notes in Computer Science 3641. Lecture Notes in Artificial Intelligence, 345-353 (2005). 2005 Berlin: Springer EN

doi:10.1007/11548669

Summary: In this paper, we study rough set approximations under fuzzy and random environments. A fuzzy set-valued mapping defines a pair of upper and lower fuzzy rough approximations. Properties of fuzzy approximation operators are examined and the crisp representations of fuzzy approximation operators are presented. A fuzzy random variable from a universe $U$ to a universe $W$ carries a probability measure defined over subsets of $U$ into a system of upper and lower probabilities over subsets of W. The connections between fuzzy approximation spaces and fuzzy belief structures are also established.