In this paper we present a fuzzy extension of description logics ALC combining C-Fuzzy set theory with a classical DL.C-Fuzzy set theory overcomes the error and the shortcoming of Zadeh's fuzzy set theory,and it is consistent with normal,natural and classical thinking,logic and concepts.In particular,concepts become fuzzy and,thus,reasoning about imprecise concepts is supported.We will define its syntax,its semantics,describe its properties and present a constraint propagation calculus for reasoning in it.
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