Abstract: This paper concerns discounted Markov decision processes with a fuzzy reward function triangular in shape.
Starting with a usual and non-fuzzy Markov control model (Hernández-Lerma, 1989) with compact action ´
sets and reward R, a control model is induced only substituting R in the usual model for a suitable triangular
fuzzy function R˜ which models, in a fuzzy sense, the fact that the reward R is “approximately” received. This
way, for this induced model a discounted optimal control problem is considered, taking into account both a
finite and an infinite horizons, and fuzzy objective functions. In order to obtain the optimal solution, the partial
order on the α-cuts of fuzzy numbers is used, and the optimal solution for fuzzy Markov decision processes
is found from the optimal solution of the corresponding usual Markov decision processes. In the end of the
paper, several examples are given to illustrate the theory developed: a model of inventory system, and two
others more in an economic and financial context.(More)

This paper concerns discounted Markov decision processes with a fuzzy reward function triangular in shape. Starting with a usual and non-fuzzy Markov control model (Hernández-Lerma, 1989) with compact action ´ sets and reward R, a control model is induced only substituting R in the usual model for a suitable triangular fuzzy function R˜ which models, in a fuzzy sense, the fact that the reward R is “approximately” received. This way, for this induced model a discounted optimal control problem is considered, taking into account both a finite and an infinite horizons, and fuzzy objective functions. In order to obtain the optimal solution, the partial order on the α-cuts of fuzzy numbers is used, and the optimal solution for fuzzy Markov decision processes is found from the optimal solution of the corresponding usual Markov decision processes. In the end of the paper, several examples are given to illustrate the theory developed: a model of inventory system, and two others more in an economic and financial context.

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Carrero-Vera, K.; Cruz-Suárez, H. and Montes-de-Oca, R. (2021). Discounted Markov Decision Processes with Fuzzy Rewards Induced by Non-fuzzy Systems. In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - ICORES, ISBN 978-989-758-485-5; ISSN 2184-4372, pages 49-59. DOI: 10.5220/0010231400490059

@conference{icores21, author={Karla Carrero{-}Vera. and Hugo Cruz{-}Suárez. and Raúl Montes{-}de{-}Oca.}, title={Discounted Markov Decision Processes with Fuzzy Rewards Induced by Non-fuzzy Systems}, booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - ICORES,}, year={2021}, pages={49-59}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0010231400490059}, isbn={978-989-758-485-5}, issn={2184-4372}, }

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - ICORES, TI - Discounted Markov Decision Processes with Fuzzy Rewards Induced by Non-fuzzy Systems SN - 978-989-758-485-5 IS - 2184-4372 AU - Carrero-Vera, K. AU - Cruz-Suárez, H. AU - Montes-de-Oca, R. PY - 2021 SP - 49 EP - 59 DO - 10.5220/0010231400490059

- Science and Technology Publications, Lda.RESOURCES