Geodesic
Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix
Kybernetika, Tome 48 (2012) no. 2, pp. 309-328 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
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     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},
     year = {2012},
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_2_a10/}
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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/