Abstract
Discrete-time discounted Markov decision processes (MDPs, in singular MDP) with finite state spaces, compact action sets and trapezoidal fuzzy reward functions are presented in this article. For such a kind of MDPs, both the finite and the infinite horizons cases are studied. The corresponding optimal control problems are established with respect to the partial order on the \(\alpha \)-cuts of fuzzy numbers, named the fuzzy max order. The fuzzy optimal solution is related to a suitable discounted MDP with a nonfuzzy reward. And in the article, different applications of the theory developed are provided: a finite-horizon model of an inventory system in which an algorithm to calculate the optimal solution is given, and, additionally for the infinite-horizon case, an MDP and a competitive MDP (also known as a stochastic game) are supplied in an economic and financial context.
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Carrero-Vera, K., Cruz-Suárez, H., Montes-de-Oca, R. (2022). Finite-Horizon and Infinite-Horizon Markov Decision Processes with Trapezoidal Fuzzy Discounted Rewards. In: Parlier, G.H., Liberatore, F., Demange, M. (eds) Operations Research and Enterprise Systems. ICORES ICORES 2020 2021. Communications in Computer and Information Science, vol 1623. Springer, Cham. https://doi.org/10.1007/978-3-031-10725-2_9
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