On the λ-robustness of matrices over fuzzy algebra

Authors:
Ján Plavka;Peter Szabó
Affiliations:
Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University, B. Nmcovej 32, 04200 Košice, Slovakia;Department of Aerodynamics and Simulations, Faculty of Aeronautics, Technical University in Košice, Rampová 7, 04200 Košice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Let (B,@?) be a non-empty, bounded, linearly ordered set and a@?b=max{a,b}, a@?b=min{a,b} for a,b@?B. A vector x is said to be a @l-eigenvector of a square matrix A if A@?x=@l@?x for some @l@?B. A given matrix A is called (strongly) @l-robust if for every x the vector A^k@?x is a (greatest) eigenvector of A for some natural number k. We present a characterization of @l-robust and strongly @l-robust matrices. Building on this, an efficient algorithm for checking the @l-robustness and strong @l-robustness of a given matrix is introduced.