Interval rough numbers play an important role in dealing with complex fuzzy relationships. In this paper, a group decision-making (GDM) model based on interval rough multiplicative reciprocal (IRMR) matrix is proposed. Firstly, the inconsistency, satisfactory consistency and complete consistency of the IRMR matrix are defined from the perspective of set theory. Secondly, an improved method for the inconsistent IRMR matrix is introduced to address the inconsistent preference matrix in GDM. We define the uniform approximation matrix of the IRMR matrix, prove its existence, and provide a new calculation method for the sorting vector of IRMR matrix. Finally, the multiplicative reciprocal matrix obtained with a weighted geometric operator assembly is still the IRMR matrix. A GDM algorithm of the IRMR matrix is presented. The proposed algorithm is demonstrated using an illustrative example, and its feasibility and effectiveness are verified through comparison with other existing methods.

间隔粗糙数在处理复杂的模糊关系中起重要作用。本文提出了一种基于区间粗糙可乘倒数（IRMR）矩阵的群体决策模型。首先，从集合论的角度定义了IRMR矩阵的不一致，令人满意的一致性和完全一致性。其次，针对不一致的IRMR矩阵，提出了一种改进的方法来解决GDM中不一致的偏好矩阵。定义了IRMR矩阵的统一逼近矩阵，证明了它的存在性，为IRMR矩阵的排序向量提供了一种新的计算方法。最后，通过加权几何算子组合获得的可逆矩阵仍然是IRMR矩阵。提出了IRMR矩阵的GDM算法。