Markov decision processes on finite spaces with fuzzy total rewards

Title:

Markov decision processes on finite spaces with fuzzy total rewards

Creator:

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

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8fb46b07-09bf-4d02-b7cd-a060c8736a3e
uuid:8fb46b07-09bf-4d02-b7cd-a060c8736a3e
doi:10.14736/kyb-2022-2-0180

Subject:

Markov decision process, total reward, fuzzy reward, trapezoidal fuzzy number, optimal stopping problem, and gambling model

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 α-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.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

180-199

Source:

Kybernetika | 2022 Volume:58 | Number:2

Harvested from:

CDK

Metadata only:

false