AE and EA versions of X -robustness for interval circulant matrices in max–min algebra

Abstract

Max–min algebra is defined as a linearly ordered set with two binary operations. Classical addition and multiplication are replaced by maximum and minimum, respectively. A square matrix is called robust, if all its orbits converge to an eigenvector. In practice, matrix inputs and start vector inputs are rather contained in some intervals than exact values. Considering matrices and vectors with interval coefficients is therefore of great practical importance. In this paper, we study a special type of the robustness called the -robustness, the case when a starting vector is limited by a lower bound vector and an upper bound vector . If we consider some components of the interval starting vector with the existential quantifier and others with the general quantifier, two new types of -robustness arise, called -robustness and -robustness. Using a similar quantification of interval matrix elements, we obtain AE/EA--robustness and AE/EA--robustness. A complete characterization of AE/EA--robustness and AE/EA--robustness for a special type of interval matrices, so-called interval circulant matrices, is presented.