Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix

Imran Rashid; Martin Gavalec; Sergeĭ Sergeev

Kybernetika (2012)

  • Volume: 48, Issue: 2, page 309-328
  • ISSN: 0023-5954

Abstract

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Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6.

How to cite

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Rashid, Imran, Gavalec, Martin, and Sergeev, Sergeĭ. "Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix." Kybernetika 48.2 (2012): 309-328. <http://eudml.org/doc/246141>.

@article{Rashid2012,
abstract = {Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6.},
author = {Rashid, Imran, Gavalec, Martin, Sergeev, Sergeĭ},
journal = {Kybernetika},
keywords = {Łukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector; Łukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector},
language = {eng},
number = {2},
pages = {309-328},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix},
url = {http://eudml.org/doc/246141},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Rashid, Imran
AU - Gavalec, Martin
AU - Sergeev, Sergeĭ
TI - Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 2
SP - 309
EP - 328
AB - Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6.
LA - eng
KW - Łukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector; Łukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector
UR - http://eudml.org/doc/246141
ER -

References

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