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In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix A is called strongly robust if the orbit x;A x;A2 x;: :: reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong X-robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition for the strong X-robustness is introduced and efficient algorithms for verifying the strong X-robustness is described. The strong X-robustness of a max-min matrix is extended to interval vectors X and interval matrices A using for-all-exists quantification of their interval and matrix entries. A complete characterization of AE/EA strong X-robustness of interval circulant matrices is presented. [ABSTRACT FROM AUTHOR]

A matrix A is said to have X-simple image eigenspace if any eigenvector x belonging to the interval X = fx: x ≤ x ≤ xg containing a constant vector is the unique solution of the system A y = x in X. The main result of this paper is an extension of X-simplicity to interval max-min matrix A = fA: A ≤ A ≤ Ag distinguishing two possibilities, that at least one matrix or all matrices from a given interval have X-simple image eigenspace. X-simplicity of interval matrices in max-min algebra are studied and equivalent conditions for interval matrices which have X-simple image eigenspace are presented. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras. [ABSTRACT FROM AUTHOR]