On the weak robustness of interval fuzzy matrices

A max–min (fuzzy) matrix A   (operations max and min are denoted by ⊕ and ⊗, respectively) is called weakly robust if the only possibility to arrive at an eigenvector is to start the sequence (orbit) x,A⊗x,A2⊗x,…x,A⊗x,A2⊗x,… by a vector that is itself an eigenvector. The weak robustness of a fuzzy matrix is extended to interval fuzzy matrices distinguishing two possibilities, that at least one matrix or all matrices from a given interval are weakly robust. Characterization of weak robustness of interval fuzzy matrices is presented and an O(n3)O(n3) algorithm for checking the weak robustness of interval fuzzy matrices is described.