Kybernetika 48 no. 2, 309-328, 2012

Eigenspace of a three-dimensional max-Lukasiewicz fuzzy matrix

Imran Rashid, Martin Gavalec and Sergeĭ Sergeev


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.


Łukasiewicz triangular norm, max-t fuzzy algebra, eigenproblem, monotone eigenvector


93E12, 62A10


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