Fuzzy decision processes with time-average fuzzy rewards

Deals with a multi-stage decision process with fuzzy transitions, which is termed a `fuzzy decision process´. We consider such a 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. A time-average fuzzy reward for the process is described by a fuzzy number; and a partial order of convex fuzzy numbers, which is called a `fuzzy max order´, is used to discuss the optimization problem. By introducing relative value functions, the optimal average reward is characterized as a unique solution of the associated equation. Further, we estimate the fuzzy rewards by introducing a fuzzy expectation that is generated by a fuzzy goal