Continuous-time fuzzy decision processes with discounted rewards

Abstract

A continuous-time decision process with fuzzy transitions, which is termed fuzzy decision process, is discussed from a viewpoint of a dynamic fuzzy system by the authors. The discounted total reward is given by a fuzzy number and is discussed by the fuzzy max order. This paper gives the optimality equation for the fuzzy decision model by a fuzzy differential equation. The optimization problem of the discounted total rewards is also discussed by a fuzzy expectation generated from a fuzzy goal, and an optimal policy and the permissible range of the decision maker's optimal expected payoffs are given for this problem. Also, an illustrated example is given to explain the idea of the paper.