In this paper, a novel optimal scale selection method in complete multi-scale decision tables has been proposed. Unlike the existing approaches in the literature, we employ the tools of granularity trees and cuts for each attribute. Each granularity tree has many different local cuts, which represent various scale selection methods under a specific attribute. Different local cuts collectively forms a global cut of a multi-scale information table, which in turn induces an information table with a mixed scale. One distinct feature of such tables is that the attribute values of different objects may be obtained at different scales for the same attribute. By keeping maximal consistency of the derived mixed-scale decision table, we introduce the notions of optimal cuts in multi-scale decision tables. Then, a comparative study between different types of optimal scale selection methods is performed. Finally, an algorithm is designed to verify the validity of the proposed approach.

本文提出了一种在完整的多尺度决策表中的最优尺度选择方法。与文献中现有的方法不同，我们为每个属性使用粒度树和切分工具。每个粒度树都有许多不同的局部切割，它们代表特定属性下的各种比例选择方法。不同的局部切割共同形成了多尺度信息表的全局切割，这又导致了一个具有混合尺度的信息表。这种表的一个独特特征是，对于同一属性，可以以不同的比例获得不同对象的属性值。通过保持导出的混合尺度决策表的最大一致性，我们在多尺度决策表中引入了最优切割的概念。然后，对不同类型的最佳标尺选择方法进行了比较研究。最后，设计了一种算法来验证所提方法的有效性。