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Authors: Karla Carrero-Vera 1 ; Hugo Cruz-Suárez 1 and Raúl Montes-de-Oca 2

Affiliations: 1 Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río Verde, Col. San Manuel, CU, Puebla, Pue. 72570, Mexico ; 2 Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Ciudad de México 09340, Mexico

Keyword(s): Markov Decision Processes, Dynamic Programming, Optimal Policy, Fuzzy Sets, Triangular Fuzzy Numbers.

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)

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Paper citation in several formats:
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

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