A fuzzy approach to Markov decision processes with uncertain transition probabilities

In this paper, a Markov decision model with uncertain transition matrices, which allow a matrix to fluctuate at each step in time, is described by the use of fuzzy sets. We find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward over all stationary policies under some partial order. The pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set-functions. As a numerical example, the machine maintenance problem is considered.