Abstract
With standard operators the fuzzy sets defined over a universe of discourse respects the structure of a De Morgan algebra. Via an injective canonical mapping we establish an isomorphism to a De Morgan algebra of crisp subsets of an extended universe. The canonical mapping gives a natural extension of any algebraic operator acting on fuzzy sets to a crisp analog. This proves that the algebraic aspects of fuzzy set theory can be completely described within the framework of crisp set theory.
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