Markov decision processes on finite spaces with fuzzy total rewards

Carrero-Vera, Karla, Cruz-Suárez, Hugo, and Montes-de-Oca, Raúl. "Markov decision processes on finite spaces with fuzzy total rewards." Kybernetika 58.2 (2022): 180-199. <http://eudml.org/doc/298894>.

@article{Carrero2022,
abstract = {The paper concerns Markov decision processes (MDPs) with both the state and the decision spaces being finite and with the total reward as the objective function. For such a kind of MDPs, the authors assume that the reward function is of a fuzzy type. Specifically, this fuzzy reward function is of a suitable trapezoidal shape which is a function of a standard non-fuzzy reward. The fuzzy control problem consists of determining a control policy that maximizes the fuzzy expected total reward, where the maximization is made with respect to the partial order on the $\alpha $-cuts of fuzzy numbers. The optimal policy and the optimal value function for the fuzzy optimal control problem are characterized by means of the dynamic programming equation of the standard optimal control problem and, as main conclusions, it is obtained that the optimal policy of the standard problem and the fuzzy one coincide and the fuzzy optimal value function is of a convenient trapezoidal form. As illustrations, fuzzy extensions of an optimal stopping problem and of a red-black gambling model are presented.},
author = {Carrero-Vera, Karla, Cruz-Suárez, Hugo, Montes-de-Oca, Raúl},
journal = {Kybernetika},
keywords = {Markov decision process; total reward; fuzzy reward; trapezoidal fuzzy number; optimal stopping problem; gambling model},
language = {eng},
number = {2},
pages = {180-199},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Markov decision processes on finite spaces with fuzzy total rewards},
url = {http://eudml.org/doc/298894},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Carrero-Vera, Karla
AU - Cruz-Suárez, Hugo
AU - Montes-de-Oca, Raúl
TI - Markov decision processes on finite spaces with fuzzy total rewards
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 2
SP - 180
EP - 199
AB - The paper concerns Markov decision processes (MDPs) with both the state and the decision spaces being finite and with the total reward as the objective function. For such a kind of MDPs, the authors assume that the reward function is of a fuzzy type. Specifically, this fuzzy reward function is of a suitable trapezoidal shape which is a function of a standard non-fuzzy reward. The fuzzy control problem consists of determining a control policy that maximizes the fuzzy expected total reward, where the maximization is made with respect to the partial order on the $\alpha $-cuts of fuzzy numbers. The optimal policy and the optimal value function for the fuzzy optimal control problem are characterized by means of the dynamic programming equation of the standard optimal control problem and, as main conclusions, it is obtained that the optimal policy of the standard problem and the fuzzy one coincide and the fuzzy optimal value function is of a convenient trapezoidal form. As illustrations, fuzzy extensions of an optimal stopping problem and of a red-black gambling model are presented.
LA - eng
KW - Markov decision process; total reward; fuzzy reward; trapezoidal fuzzy number; optimal stopping problem; gambling model
UR - http://eudml.org/doc/298894
ER -