Discounted Markov decision processes with fuzzy costs

Salvador De-Jesús-Hernández; Hugo Cruz-Suárez; Raúl Montes-de-Oca

Kybernetika (2025)

  • Issue: 1, page 58-78
  • ISSN: 0023-5954

Abstract

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This article concerns a class of discounted Markov decision processes on Borel spaces where, in contrast with the classical framework, the cost function C ˜ is a fuzzy function of a trapezoidal type, which is determined from a classical cost function C by applying an affine transformation with fuzzy coefficients. Under certain conditions ensuring that the classical (or standard) model with a cost function C has an optimal stationary policy f o with the optimal cost V o , it is shown that such a policy is also optimal for the fuzzy model with a cost function C ˜ , and that the optimal fuzzy value V ˜ o is obtained from V o via the same transformation used to go from C to C ˜ . And these results are obtained with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Besides, a fuzzy version of the classical linear-quadratic model without restrictions is presented.

How to cite

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De-Jesús-Hernández, Salvador, Cruz-Suárez, Hugo, and Montes-de-Oca, Raúl. "Discounted Markov decision processes with fuzzy costs." Kybernetika (2025): 58-78. <http://eudml.org/doc/299935>.

@article{De2025,
abstract = {This article concerns a class of discounted Markov decision processes on Borel spaces where, in contrast with the classical framework, the cost function $\widetilde\{C\}$ is a fuzzy function of a trapezoidal type, which is determined from a classical cost function $C$ by applying an affine transformation with fuzzy coefficients. Under certain conditions ensuring that the classical (or standard) model with a cost function $C$ has an optimal stationary policy $f_\{o\}$ with the optimal cost $V_\{o\}$, it is shown that such a policy is also optimal for the fuzzy model with a cost function $\widetilde\{C\}$, and that the optimal fuzzy value $\tilde\{V\}_\{o\}$ is obtained from $V_\{o\}$ via the same transformation used to go from $C$ to $\widetilde\{C\}$. And these results are obtained with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Besides, a fuzzy version of the classical linear-quadratic model without restrictions is presented.},
author = {De-Jesús-Hernández, Salvador, Cruz-Suárez, Hugo, Montes-de-Oca, Raúl},
journal = {Kybernetika},
keywords = {discounted Markov decision processes; trapezoidal fuzzy costs; max-order; average ranking},
language = {eng},
number = {1},
pages = {58-78},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Discounted Markov decision processes with fuzzy costs},
url = {http://eudml.org/doc/299935},
year = {2025},
}

TY - JOUR
AU - De-Jesús-Hernández, Salvador
AU - Cruz-Suárez, Hugo
AU - Montes-de-Oca, Raúl
TI - Discounted Markov decision processes with fuzzy costs
JO - Kybernetika
PY - 2025
PB - Institute of Information Theory and Automation AS CR
IS - 1
SP - 58
EP - 78
AB - This article concerns a class of discounted Markov decision processes on Borel spaces where, in contrast with the classical framework, the cost function $\widetilde{C}$ is a fuzzy function of a trapezoidal type, which is determined from a classical cost function $C$ by applying an affine transformation with fuzzy coefficients. Under certain conditions ensuring that the classical (or standard) model with a cost function $C$ has an optimal stationary policy $f_{o}$ with the optimal cost $V_{o}$, it is shown that such a policy is also optimal for the fuzzy model with a cost function $\widetilde{C}$, and that the optimal fuzzy value $\tilde{V}_{o}$ is obtained from $V_{o}$ via the same transformation used to go from $C$ to $\widetilde{C}$. And these results are obtained with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Besides, a fuzzy version of the classical linear-quadratic model without restrictions is presented.
LA - eng
KW - discounted Markov decision processes; trapezoidal fuzzy costs; max-order; average ranking
UR - http://eudml.org/doc/299935
ER -

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