| Title:
|
Strong $\mathbf {X}$-robustness of interval max-min matrices (English) |
| Author:
|
Myšková, Helena |
| Author:
|
Plavka, Ján |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
594-612 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix $A$ is called strongly robust if the orbit $x,A\otimes x, A^2\otimes x,\dots$ reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong \textit{\textbf{X}}-robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition for the strong \textit{\textbf{X}}-robustness is introduced and efficient algorithms for verifying the strong \textit{\textbf{X}}-robustness is described. The strong \textit{\textbf{X}}-robustness of a max-min matrix is extended to interval vectors \textit{\textbf{X}} and interval matrices \textit{\textbf{A}} using for-all-exists quantification of their interval and matrix entries. A complete characterization of AE/EA strong \textit{\textbf{X}}-robustness of interval circulant matrices is presented. (English) |
| Keyword:
|
max-min algebra |
| Keyword:
|
interval matrix |
| Keyword:
|
strong robustness |
| Keyword:
|
AE(EA) robustness |
| MSC:
|
15A18 |
| MSC:
|
15A80 |
| MSC:
|
93C55 |
| idZBL:
|
Zbl 07478630 |
| idMR:
|
MR4332883 |
| DOI:
|
10.14736/kyb-2021-4-0594 |
| . |
| Date available:
|
2021-11-04T12:54:39Z |
| Last updated:
|
2022-02-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149210 |
| . |
| Reference:
|
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