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Title: Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix (English)
Author: Rashid, Imran
Author: Gavalec, Martin
Author: Sergeev, Sergeĭ
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 48
Issue: 2
Year: 2012
Pages: 309-328
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Łukasiewicz triangular norm
Keyword: max-t fuzzy algebra
Keyword: eigenproblem
Keyword: monotone eigenvector
MSC: 62A10
MSC: 93E12
idMR: MR2954329
Date available: 2012-05-15T16:20:54Z
Last updated: 2013-09-22
Stable URL:
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