On the dimension of max-min convex sets

We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvability of linear systems and trapezoidal property.Comment: 19 pages, v2: many corrections in the proof

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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