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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Membership function (mathematics) ： ウィキペディア英語版 Membership function (mathematics) The membership function of a fuzzy set is a generalization of the indicator function in classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Degrees of truth are often confused with probabilities, although they are conceptually distinct, because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. Membership functions were introduced by Zadeh in the first paper on fuzzy sets (1965). Zadeh, in his theory of fuzzy sets, proposed using a membership function (with a range covering the interval (0,1)) operating on the domain of all possible values. == Definition == For any set $X$, a membership function on $X$ is any function from $X$ to the real unit interval $()$. Membership functions on $X$ represent fuzzy subsets of $X$. The membership function which represents a fuzzy set $\backslash tilde\; A$ is usually denoted by $\backslash mu\_A.$ For an element $x$ of $X$, the value $\backslash mu\_A(x)$ is called the ''membership degree'' of $x$ in the fuzzy set $\backslash tilde\; A.$ The membership degree $\backslash mu\_(x)$ quantifies the grade of membership of the element $x$ to the fuzzy set $\backslash tilde\; A.$ The value 0 means that $x$ is not a member of the fuzzy set; the value 1 means that $x$ is fully a member of the fuzzy set. The values between 0 and 1 characterize fuzzy members, which belong to the fuzzy set only partially. File:Fuzzy crisp.svg Membership function of a fuzzy set Sometimes,〔First in Goguen (1967).〕 a more general definition is used, where membership functions take values in an arbitrary fixed algebra or structure $L$; usually it is required that $L$ be at least a poset or lattice. The usual membership functions with values in () are then called ()-valued membership functions. 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「Membership function (mathematics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.