On fuzzy decision processes with discounted fuzzy rewards

Deals with a multi-stage decision process with fuzzy transitions, which is termed a 'fuzzy decision process'. We consider the fuzzy decision process, where both states and actions are assumed to be fuzzy, from the point of view of a dynamic fuzzy system which has been developed by the authors. The discounted total reward is described by a fuzzy number on a closed bounded interval. A partial order of convex fuzzy numbers, which is called a 'fuzzy max order', is used to discuss the optimization problem. We characterize the discounted total reward associated with an admissible stationary policy by a unique fixed point of the contractive mapping. Further, we estimate the fuzzy rewards by introducing a fuzzy expectation generated by a fuzzy goal.