Matrix representation of optimal scale for generalized multi-scale decision table

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.