On the λλ-robustness of matrices over fuzzy algebra

Let (B,≤)(B,≤) be a non-empty, bounded, linearly ordered set and a⊕b=max{a,b}a⊕b=max{a,b}, a⊗b=min{a,b}a⊗b=min{a,b} for a,b∈Ba,b∈B. A vector xx is said to be a λλ-eigenvector of a square matrix AA if A⊗x=λ⊗xA⊗x=λ⊗x for some λ∈Bλ∈B. A given matrix AA is called (strongly) λλ-robust if for every xx the vector Ak⊗xAk⊗x is a (greatest) eigenvector of AA for some natural number kk. We present a characterization of λλ-robust and strongly λλ-robust matrices. Building on this, an efficient algorithm for checking the λλ-robustness and strong λλ-robustness of a given matrix is introduced.