The article presents an extension of the theory of standard Markov decision processes on discrete spaces and with the average cost as the objective function which permits to take into account a fuzzy average cost of a trapezoidal type. In this context, the fuzzy optimal control problem is considered with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Each of these cases extends the standard optimal control problem, and for each of them the optimal solution is related to a suitable standard optimal control problem, and it is obtained that (i) the optimal policy coincides with the optimal policy of this suitable standard control problem, and (ii) the fuzzy optimal value function is of a trapezoidal shape. Two models: a queueing system and a machine replacement problem are provided in order to examplify the theory given.
Markov decision process, average criterion, trapezoidal fuzzy cost, max-order, average ranking