| Title:
|
Discounted Markov decision processes with fuzzy costs (English) |
| Author:
|
De-Jesús-Hernández, Salvador |
| Author:
|
Cruz-Suárez, Hugo |
| Author:
|
Montes-de-Oca, Raúl |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
58-78 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
discounted Markov decision processes |
| Keyword:
|
trapezoidal fuzzy costs |
| Keyword:
|
max-order |
| Keyword:
|
average ranking |
| MSC:
|
90C40 |
| MSC:
|
93C42 |
| DOI:
|
10.14736/kyb-2025-1-0058 |
| . |
| Date available:
|
2025-04-07T09:37:36Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152925 |
| . |
| Reference:
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