Fuzzy Dynamic Programming with Stochastic Systems

Multistage decision making in a fuzzy environment (fuzzy constraints, fuzzy goals and fuzzy decisions) is considered. As a tool for solving these problems, fuzzy dynamic programming for the case of a deterministic and fuzzy system under control is provided. Then, the case of a stochastic system under control is discussed in detail. Two formulations are shown: first, the classic one due to Bellman and Zadeh (1970) in which an optimal sequence of controls is sought to maximize the probability of attainment of a fuzzy goal subject to fuzzy constraints, and second, an alternative one due to Kacprzyk and Staniewski (1980) in which an optimal sequence of controls is sought to maximize the expected value of the fuzzy decision.

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