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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 Uncertainty theory ： ウィキペディア英語版 Uncertainty theory Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. It was founded by Baoding Liu 〔Baoding Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.〕 in 2007 and refined in 2009.〔Baoding Liu, Uncertainty Theory, 4th ed., http://orsc.edu.cn/liu/ut.pdf.〕 Mathematical measures of the likelihood of an event being true include probability theory, capacity, fuzzy logic, possibility, and credibility, as well as uncertainty. ==Five axioms== Axiom 1. (Normality Axiom) $\backslash mathcal\backslash =1\backslash text\backslash Gamma$. Axiom 2. (Monotonicity Axiom) $\backslash mathcal\backslash \backslash le\backslash mathcal\backslash \backslash text\backslash Lambda\_1\backslash subset\backslash Lambda\_2$. Axiom 3. (Self-Duality Axiom) $\backslash mathcal\backslash +\backslash mathcal\backslash =1\backslash text\backslash Lambda$. Axiom 4. (Countable Subadditivity Axiom) For every countable sequence of events Λ1, Λ2, ..., we have ::$\backslash mathcal\backslash left\backslash \backslash le\backslash sum\_^\backslash infty\backslash mathcal\backslash$. Axiom 5. (Product Measure Axiom) Let $(\backslash Gamma\_k,\backslash mathcal\_k,\backslash mathcal\_k)$ be uncertainty spaces for $k=1,2,\backslash cdots,n$. Then the product uncertain measure $\backslash mathcal$ is an uncertain measure on the product σ-algebra satisfying ::$\backslash mathcal\backslash left\backslash =\backslash underset\backslash mathcal\_i\backslash$. Principle. (Maximum Uncertainty Principle) For any event, if there are multiple reasonable values that an uncertain measure may take, then the value as close to 0.5 as possible is assigned to the event. 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「Uncertainty theory」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.