Controlled Markov set-chains under average criteria

In this paper, applying an interval arithmetic analysis, we consider the average case of controlled Markov set-chains, whose process allows for fluctuating transition matrices at each step in time. We introduce an a-step contractive property for the average case, under which a Pareto optimal periodic policy is characterized as a maximal solution of optimality equation. Also, in the class of stationary policies, the behavior of the expected reward over T-horizon as T approaches infinity is investigated and the left- and right-hand side optimality equations are given, by which a Pareto optimal stationary policy is found. As a numerical example, the Taxicab problem is considered.