Abstract
In this paper, the average case of finite state controlled Markov set‐chains with Rp‐set‐valued rewards are considered. The optimization is done by a pseudo‐order relation on the set of all convex and compact subsets of Rp induced by a closed convex cone. We introduce a v‐step contractive property (minorization condition) for the average case and by use of this method the average expected reward set from a periodic policy is characterized. And, applying the scalarization technique, a Pareto optimal policy is obtained. Also, a numerical example is given to comprehend our results.
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