The Fuzzy set reference article from the English Wikipedia on 24-Jul-2004
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Fuzzy set

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Fuzzy sets are an extension of the classical set theory used in Fuzzy logic. A fuzzy set is characterized by a membership-degree function, which maps the members of the Universe into the unit interval [0,1]. The value 0 means that the member is not included in the given set, 1 describes a fully included member (this behaviour corresponds to the indicator function of classical sets). The values between 0 and 1 characterize fuzzy members.

For the universe X and given the membership-degree function f : X→[0,1], the fuzzy set A is defined as A = {(x, f(x)) | x ∈ X}.