Markov decision processes with fuzzy rewards

In this paper, we consider the model that the information on the rewards in vector-valued Markov decision processes includes imprecision or ambiguity. The fuzzy reward model is analyzed as follows: The fuzzy reward is represented by the fuzzy set on the multi-dimensional Euclidian space R and the infinite horizon fuzzy expected discounted reward(FEDR) from any stationary policy is characterized as a unique fixed point of the corresponding contractive operator. Also, we fined a Pareto optimal policy which maximizes the infinite horizon FEDR over all stationary policies under the pseudo order induced by a convex cone R. As a numerical example, the machine maintenance problem is considered.

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