The Markov Decision Process in Fuzzy Events

In this paper, we considered decision processes in which one decision is made in each process. We incorporate the utility function concept into the decision process, derived the utility function in fuzzy events and by the max-product operation obtained the utility possibility measure of the fuzzy events. In cases with numerous decision processes, the optimum action can be determined from the relative size of the possibility measures, while in cases with observation information in each process, a single compromise possibility measure can be obtained by identifying the observation information in terms of type-2 fuzzy events that envelop the upper and lower sides and then incorporating the two fuzzy goals into a two-objective non-linear programming problem that minimizes the possibility measure on the upper side and maximizes the possibility measure on the lower side. Among the resulting compromise solutions, we proposed taking the one with the largest possibility measure as the optimum action.