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Keywords:
discounted Markov decision processes; trapezoidal fuzzy costs; max-order; average ranking
discounted Markov decision processes; trapezoidal fuzzy costs; max-order; average ranking
Summary:
This article concerns a class of discounted Markov decision processes on Borel spaces where, in contrast with the classical framework, the cost function $\widetilde C$ is a fuzzy function of a trapezoidal type, which is determined from a classical cost function $C$ by applying an affine transformation with fuzzy coefficients. Under certain conditions ensuring that the classical (or standard) model with a cost function $C$ has an optimal stationary policy $f_{o}$ with the optimal cost $V_{o}$, it is shown that such a policy is also optimal for the fuzzy model with a cost function $\widetilde C$, and that the optimal fuzzy value $\tilde{V}_{o}$ is obtained from $V_{o}$ via the same transformation used to go from $C$ to $\widetilde C$. And these results are obtained with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Besides, a fuzzy version of the classical linear-quadratic model without restrictions is presented.
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