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Fuzzy subalgebras theory is a chapter of fuzzy set theory. It is obtained from an interpretation in a multi-valued logic of axioms usually expressing the notion of subalgebra of a given algebraic structure. == Definition == Consider a first order language for algebraic structures with a monadic predicate symbol S. Then a ''fuzzy subalgebra'' is a fuzzy model of a theory containing, for any ''n''-ary operation h, the axioms and, for any constant c, S(c). The first axiom expresses the closure of S with respect to the operation h, and the second expresses the fact that c is an element in S. As an example, assume that the valuation structure is defined in () and denote by the operation in () used to interpret the conjunction. Then a fuzzy subalgebra of an algebraic structure whose domain is D is defined by a fuzzy subset of D such that, for every d1,...,dn in D, if h is the interpretation of the n-ary operation symbol h, then * Moreover, if c is the interpretation of a constant c such that s(c) = 1. A largely studied class of fuzzy subalgebras is the one in which the operation coincides with the minimum. In such a case it is immediate to prove the following proposition. Proposition. A fuzzy subset s of an algebraic structure defines a fuzzy subalgebra if and only if for every λ in (), the closed cut of s is a subalgebra. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fuzzy subalgebra」の詳細全文を読む スポンサード リンク
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