Traditional rough set approach is mainly used to unravel rules from a decision table in which objects can possess a unique attribute-value. In a real world data set, for the same attribute objects are usually measured at different scales. The main objective of this paper is to study optimal scale combinations in generalized multi-scale decision tables. A generalized multi-scale information table is an attribute-value system in which different attributes are measured at different levels of scales. With the aim of investigating knowledge representation and knowledge acquisition in inconsistent generalized multi-scale decision tables, we first introduce the notion of scale combinations in a generalized multi-scale information table. We then formulate information granules with different scale combinations in multi-scale information systems and discuss their relationships. Furthermore, we define lower and upper approximations of sets with different scale combinations and examine their properties. Finally, we examine optimal scale combinations in inconsistent generalized multi-scale decision tables. We clarify relationships among different concepts of optimal scale combinations in inconsistent generalized multi-scale decision tables.

中文翻译：

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广义多尺度决策表中最优尺度组合选择的比较研究

传统的粗糙集方法主要用于从决策表中解散规则，其中对象可以拥有唯一的属性值。在现实世界的数据集中，对于相同的属性对象，通常以不同的比例尺进行测量。本文的主要目的是研究广义多尺度决策表中的最优尺度组合。广义的多尺度信息表是一种属性值系统，其中在不同的尺度级别上测量不同的属性。为了研究不一致的广义多尺度决策表中的知识表示和知识获取，我们首先在广义多尺度信息表中引入尺度组合的概念。然后，我们在多尺度信息系统中制定具有不同尺度组合的信息颗粒，并讨论它们之间的关系。此外，我们定义了具有不同比例组合的集合的上下近似，并检查了它们的性质。最后，我们在不一致的广义多尺度决策表中检查最优尺度组合。我们在不一致的广义多尺度决策表中阐明最优尺度组合的不同概念之间的关系。