Generalized multi-scale decision tables with multi-scale decision attributes

Abstract In many practical problems, games between conditions (costs) and decisions (goals) at different scales have often been encountered. Obtaining acceptable decisions under weaker conditions is one of the main tasks in the field of data analysis. However, the decision attribute has only one scale in the existing decision tables, resulting in the knowledge representation based on the framework of single decision scale being far from meeting the needs of practical applications. To overcome this drawback, this article introduces multi-scale decision information into the decision tables for the first time and proposes the generalized multi-scale decision tables. To this end, we first construct a theoretical framework of the generalized multi-scale decision tables and explore some basic properties and theorems. We then define the optimal scale in the generalized multi-scale decision tables and present two selection algorithms of optimal scale. Finally, knowledge acquisition in the sense of rule induction in generalized multi-scale decision tables is discussed. The method proposed here may improve the theoretical framework of the multi-scale decision tables and significantly expand the application of decision tables.