Fuzzy set

Fuzzy sets are an extension of the classical set theory. A fuzzy set is characterized by a membership-degree function, which maps the members of the universe into the real continuous 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 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}.