On the weak robustness of fuzzy matrices

Ján Plavka

Kybernetika (2013)

  • Volume: 49, Issue: 1, page 128-140
  • ISSN: 0023-5954

Abstract

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A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k ⊗ x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

How to cite

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Plavka, Ján. "On the weak robustness of fuzzy matrices." Kybernetika 49.1 (2013): 128-140. <http://eudml.org/doc/252482>.

@article{Plavka2013,
abstract = {A matrix $A$ in $(\max ,\min )$-algebra (fuzzy matrix) is called weakly robust if $A^k\otimes x $ is an eigenvector of $A$ only if $x$ is an eigenvector of $A$. The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an $O(n^2)$ algorithm for checking the weak robustness is described.},
author = {Plavka, Ján},
journal = {Kybernetika},
keywords = {weak robustness; fuzzy matrices; weak robustness; fuzzy matrices; fuzzy discrete dynamic systems; eigenvector; polynomial algorithm; fuzzy algebra; eigenspace; orbit; permutation marices; Hamiltonian permutation matrices},
language = {eng},
number = {1},
pages = {128-140},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the weak robustness of fuzzy matrices},
url = {http://eudml.org/doc/252482},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Plavka, Ján
TI - On the weak robustness of fuzzy matrices
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 128
EP - 140
AB - A matrix $A$ in $(\max ,\min )$-algebra (fuzzy matrix) is called weakly robust if $A^k\otimes x $ is an eigenvector of $A$ only if $x$ is an eigenvector of $A$. The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an $O(n^2)$ algorithm for checking the weak robustness is described.
LA - eng
KW - weak robustness; fuzzy matrices; weak robustness; fuzzy matrices; fuzzy discrete dynamic systems; eigenvector; polynomial algorithm; fuzzy algebra; eigenspace; orbit; permutation marices; Hamiltonian permutation matrices
UR - http://eudml.org/doc/252482
ER -

References

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Citations in EuDML Documents

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  1. Ján Plavka, Sergeĭ Sergeev, Characterizing matrices with 𝐗 -simple image eigenspace in max-min semiring
  2. Ján Plavka, Štefan Berežný, -simplicity of interval max-min matrices
  3. Matej Gazda, Ján Plavka, Controllable and tolerable generalized eigenvectors of interval max-plus matrices
  4. Ján Plavka, Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra
  5. Martin Gavalec, Helena Myšková, Ján Plavka, Daniela Ponce, Tolerance problems for generalized eigenvectors of interval fuzzy matrices

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