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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 Choquet integral ： ウィキペディア英語版 Choquet integral A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event. It is applied specifically to membership functions and capacities. In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the upper expectation induced by a 2-alternating upper probability. Using the Choquet integral to denote the expected utility of belief functions measured with capacities is a way to reconcile the Ellsberg paradox and the Allais paradox.〔Sriboonchita, S., Wong, W. K., Dhompongsa, S., & Nguyen, H. T. (2010). Stochastic dominance and applications to finance, risk and economics. CRC Press.〕 ==Definition== The following notation is used: * $S$ - a set. * $\backslash mathcal$ - a collection of subsets of $S$. * $f\; :\; S\backslash to\; \backslash mathbb$ - a function. * $\backslash nu\; :\; \backslash mathcal\backslash to\; \backslash mathbb^+$ - a monotone set function. Assume that $f$ is measurable with respect to $\backslash nu$, that is :$\backslash forall\; x\backslash in\backslash mathbb\backslash colon\; \backslash \backslash in\backslash mathcal$ Then the Choquet integral of $f$ with respect to $\backslash nu$ is defined by: :$$ (C)\int f d\nu := \int_^0 (\nu (\)-\nu(S))\, dx + \int^\infty_0 \nu (\)\, dx where the integrals on the right-hand side are the usual Riemann integral (the integrands are integrable because they are monotone in $x$). 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「Choquet integral」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.