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Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix

Imran Rashid, Martin Gavalec, Sergeĭ Sergeev (2012)


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...

On the weak robustness of fuzzy matrices

Ján Plavka (2013)


A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

Solving systems of two–sided (max, min)–linear equations

Martin Gavalec, Karel Zimmermann (2010)


A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

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