Geodesic
Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix
Kybernetika, Tome 48 (2012) no. 2, pp. 309-328.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 62A10, 93E12
Keywords: Łukasiewicz triangular norm; max-t fuzzy algebra; eigenproblem; monotone eigenvector 
@article{KYB_2012__48_2_a10,
     author = {Rashid, Imran and Gavalec, Martin and Sergeev, Serge\u{i}},
     title = {Eigenspace of a three-dimensional {max-{\L}ukasiewicz} fuzzy matrix},
     journal = {Kybernetika},
     pages = {309--328},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2012},
     mrnumber = {2954329},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a10/}
}
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
SP  - 309
EP  - 328
VL  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a10/
LA  - en
ID  - KYB_2012__48_2_a10
ER  - 
%0 Journal Article
%A Rashid, Imran
%A Gavalec, Martin
%A Sergeev, Sergeĭ
%T Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix
%J Kybernetika
%D 2012
%P 309-328
%V 48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a10/
%G en
%F KYB_2012__48_2_a10
Rashid, Imran; Gavalec, Martin; Sergeev, Sergeĭ. Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix. Kybernetika, Tome 48 (2012) no. 2, pp. 309-328. http://geodesic.mathdoc.fr/item/KYB_2012__48_2_a10/