Fuzzy Dynamic Programming

概要

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We make a survey of fuzzy dynamic programming on the basis of Bellman and Zadeh's seminal paper "Decision-making in a fuzzy environment". Our principle is that any dynamic programming must generate an optimal solution to a given problem. From this viewpoint, we propose dynamic programming method on determinstic, stochastic, and fuzzy systems. On the stochastic system, it is formulated as a maximization problem of expected value of minimum criterion not over the conventional Markov policy class but over three new broad policy classes. We present three dynamic programming approaches - (1) membership-parametric method, (2) history-parametric method, and (3) decision tree-table method -, which yield a common optimal policy in a broad (general policy) class. A complete set of optimal solutions for Bellman and Zadeh's model is illustrated. Two conditional decision processes are introduced, one of which turns out to be the Bellman and Zadeh's decision process on stochastic system. Further, a threshold-membership criterion problem is solved through fuzzy dynamic programming.
社団法人日本オペレーションズ・リサーチ学会の論文
2001-09-11