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

中文翻译：

---

具有 Monge 性质的区间矩阵

摘要。我们将实矩阵的 Monge 性质推广到区间矩阵。我们在强和弱的意义上定义了两类具有 Monge 性质的区间矩阵。我们研究这两个类的基本属性。我们展示了强 Monge 属性的几种不同特征。对于弱 Monge 性质，我们给出多项式表征和几个充分必要条件。对于这两个类，我们研究闭包属性。我们进一步提出了 Deineko & Filonenko 的算法的泛化，该算法对于给定的矩阵返回行和列排列，如果排列存在，则排列的矩阵是 Monge。