Generalized multi-scale decision table is an important model in granular computing, which can be applied to feature selection and rule extraction. The generalization effect of the model is different at different scales, so scale selection is a key to generalized multi-scale decision table. However, in existing studies, scale selection is usually based on a large number of set operations, and for different types of attributes, the model cannot be directly operated. In this paper, we first investigate the generalized multi-scale information table from the perspective of matrix. Then the matrix representation of generalized multi-scale information table is proposed. Finally, we study the properties of the matrix about the optimal scale of the coordinated and uncoordinated systems respectively, so as to give the matrix method of the scale selection. Compared with traditional methods, the matrix method presented in this paper is simple and profound, and can directly deal with different types of attributes. In addition, the matrix representation of the optimal scale has certain guiding significance for the design of the scale selection algorithm.

广义多尺度决策表是粒度计算中的重要模型，可以应用于特征选择和规则提取。该模型的泛化效果在不同尺度下有所不同，因此尺度选择是广义多尺度决策表的关键。但是，在现有研究中，尺度选择通常基于大量的设置操作，并且对于不同类型的属性，无法直接操作模型。在本文中，我们首先从矩阵的角度研究广义多尺度信息表。然后提出了广义多尺度信息表的矩阵表示。最后，我们分别研究了协调系统和非协调系统最优尺度下矩阵的性质，从而给出了尺度选择的矩阵方法。与传统方法相比，本文提出的矩阵方法简单而深刻，可以直接处理不同类型的属性。另外，最优尺度的矩阵表示对尺度选择算法的设计具有一定的指导意义。