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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 Wald's maximin model ： ウィキペディア英語版 Wald's maximin model In decision theory and game theory, Wald's maximin model is a non-probabilistic decision-making model according to which decisions are ranked on the basis of their worst-case outcomes. That is, the best (optimal) decision is one whose worst outcome is at least as good as the worst outcome of any other decisions. It is one of the most important models in robust decision making in general and robust optimization in particular. It is also known by a variety of other titles, such as Wald's maximin rule, Wald's maximin principle, Wald's maximin paradigm, and Wald's maximin criterion. Often 'minimax' is used instead of 'maximin'. ==Definition== Wald's generic maximin model is as follows: :$v^:=\; \backslash max\_\backslash min\_f(d,s)$ where $D$ denotes the decision space; $S(d)$ denotes the set of states associated with decision $d$ and $f(d,s)$ denotes the payoff (outcome) associated with decision $d$ and state $s$. This model represents a 2-person game in which the $\backslash max$ player plays first. In response, the second player selects the worst state in $S(d)$, namely a state in $S(d)$ that minimizes the payoff $f(d,s)$ over $s$ in $S(d)$. In many applications the second player represents uncertainty. However, there are maximin models that are completely deterministic. The above model is the ''classic'' format of Wald's maximin model. There is an equivalent mathematical programming (MP) format: :$v^:=\; \backslash max\_$ where $\backslash mathbb$ denotes the real line. As in game theory, the worst payoff associated with decision $d$, namely : $v(d):=\; \backslash min\_\; f(d,s)\backslash \; ,\; \backslash \; d\; \backslash in\; D$ is called ''the security level'' of decision $d$. The minimax version of the model is obtained by exchanging the positions of the $\backslash max$ and $\backslash min$ operations in the classic format: :$v^:=\; \backslash min\_\backslash max\_f(d,s).$ The equivalent MP format is as follows: :$v^:=\; \backslash min\_$ 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「Wald's maximin model」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.