Fuzzy Sets
نویسنده
چکیده
A fuzzy subset of a universe X (a fuzzy set) is a mathematical object A described by its (generalized) characteristic function (membership function) μA : X → [0, 1] Alternative notation: A(x) In this context, “classical” sets are called crisp or sharp. F(X) denotes the set of all fuzzy subsets of a universe X Range (level set): Range(A) = { α ∈ [0, 1] : (∃x ∈ X : μA(x) = α) } = μA(X) Height: h(A) = sup Range(A) Support: Supp(A) = { x ∈ X : μA(x) > 0 } = μ−1 A ( (0, 1] )
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