Kybernetika 57 no. 4, 594-612, 2021

Strong X-robustness of interval max-min matrices

Helena Myšková and Ján PlavkaDOI: 10.14736/kyb-2021-4-0594

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 \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.

Keywords:

interval matrix, max-min algebra, strong robustness, AE(EA) robustness

Classification:

15A18, 15A80, 93C55

paper.pdf

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