On the λ-robustness of matrices over fuzzy algebra

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Abstract

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

Keywords

Eigenproblem
λ-robustness
Fuzzy algebra

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