Abstract: Interval rough number judgment matrix has the dual characteristics of retaining partial deterministic judgment in uncertain judgment. However, there are few studies on it, especially on its consistency. The concept of perfect consistency and strong consistency of complementary judgment matrix based on interval rough numbers are proposed. And some theorems for judging whether they have complete consistency and strong consistency are given. The effect that internal consistency and external consistency influence on the whole consistency is discussed and some examples are given. And the relation between perfect consistency and strong consistency of complementary judgment matrix based on interval rough numbers is explained. This paper discusses the consistency theory basis for the application of interval rough number judgment matrix.

Key words: interval rough numbers, complementary judgment matrix, consistency, priority

摘要： 区间粗糙数判断矩阵具有在不确定判断中保留部分确定判断的双重特性，然而目前对其研究相对较少，特别是对其一致性的相关研究。为此该文提出了区间粗糙数互补判断矩阵的完全一致性和强一致性的概念以及判断其是否具有完全一致性和强一致性的相关定理。通过算例讨论了内外一致性对于整体一致性的影响，并给出区间粗糙数判断矩阵的完全一致性和强一致性的关系，为区间粗糙数判断矩阵的应用提供一致性理论基础作出相应探讨。

关键词: 区间粗糙数, 互补判断矩阵, 一致性, 排序