Discounted Markov Decision Processes with Fuzzy Rewards Induced by Non-fuzzy Systems

Karla Carrero-Vera, Hugo Cruz-Suárez, Raúl Montes-de-Oca

2021

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.

Paper Citation

in Harvard Style

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 - Volume 1: ICORES, ISBN 978-989-758-485-5, pages 49-59. DOI: 10.5220/0010231400490059

in Bibtex Style

@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 - Volume 1: ICORES,},
year={2021},
pages={49-59},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010231400490059},
isbn={978-989-758-485-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Discounted Markov Decision Processes with Fuzzy Rewards Induced by Non-fuzzy Systems
SN - 978-989-758-485-5
AU - Carrero-Vera K.
AU - Cruz-Suárez H.
AU - Montes-de-Oca R.
PY - 2021
SP - 49
EP - 59
DO - 10.5220/0010231400490059