Strong 𝐗 -robustness of interval max-min matrices

Helena Myšková; Ján Plavka

Kybernetika (2021)

  • Volume: 57, Issue: 4, page 594-612
  • ISSN: 0023-5954

Abstract

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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 ⊗ x , A 2 ⊗ x , ⋯ reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong 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 X-robustness is introduced and efficient algorithms for verifying the strong X-robustness is described. The strong X-robustness of a max-min matrix is extended to interval vectors X and interval matrices A using for-all-exists quantification of their interval and matrix entries. A complete characterization of AE/EA strong X-robustness of interval circulant matrices is presented.

How to cite

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Myšková, Helena, and Plavka, Ján. "Strong $\mathbf {X}$-robustness of interval max-min matrices." Kybernetika 57.4 (2021): 594-612. <http://eudml.org/doc/297506>.

@article{Myšková2021,
abstract = {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 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 X-robustness is introduced and efficient algorithms for verifying the strong X-robustness is described. The strong X-robustness of a max-min matrix is extended to interval vectors X and interval matrices A using for-all-exists quantification of their interval and matrix entries. A complete characterization of AE/EA strong X-robustness of interval circulant matrices is presented.},
author = {Myšková, Helena, Plavka, Ján},
journal = {Kybernetika},
keywords = {max-min algebra; interval matrix; strong robustness; AE(EA) robustness},
language = {eng},
number = {4},
pages = {594-612},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Strong $\mathbf \{X\}$-robustness of interval max-min matrices},
url = {http://eudml.org/doc/297506},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Myšková, Helena
AU - Plavka, Ján
TI - Strong $\mathbf {X}$-robustness of interval max-min matrices
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 4
SP - 594
EP - 612
AB - 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 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 X-robustness is introduced and efficient algorithms for verifying the strong X-robustness is described. The strong X-robustness of a max-min matrix is extended to interval vectors X and interval matrices A using for-all-exists quantification of their interval and matrix entries. A complete characterization of AE/EA strong X-robustness of interval circulant matrices is presented.
LA - eng
KW - max-min algebra; interval matrix; strong robustness; AE(EA) robustness
UR - http://eudml.org/doc/297506
ER -

References

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