  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.
