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

### Karla Carrero-Vera, Hugo Cruz-SuÃ¡rez, RaÃºl Montes-de-Oca

#### 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 (HernÃ¡ndez-Lerma, 1989) with compact action Â´ sets and reward R, a control model is induced only substituting R in the usual model for a suitable triangular fuzzy function RËœ which models, in a fuzzy sense, the fact that the reward R is â€œapproximatelyâ€ 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 Î±-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.

Download#### Paper Citation

#### in Harvard Style

Carrero-Vera K., Cruz-SuÃ¡rez 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-SuÃ¡rez and RaÃºl 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-SuÃ¡rez H.

AU - Montes-de-Oca R.

PY - 2021

SP - 49

EP - 59

DO - 10.5220/0010231400490059