Abstract
We generalize the Monge property of real matrices for interval matrices. We define two classes of interval matrices with the Monge property-in a strong and a weak sense.
We study the fundamental properties of both types. We show several different characterizations of the strong Monge property.
For the weak Monge property, we give a polynomial description and several sufficient and necessary conditions. For both classes, we study closure properties.
We further propose a generalization of an algorithm by Deineko and Filonenko which for a given matrix returns row and column permutations such that the permuted matrix is Monge if the permutations exist.