Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions.

It has been recognized that optimal scale selection in rough set theory is one of the most important problems in the study of multi-scale decision tables. Recently, much attention has been paid to this issue and quite a few appealing results have been obtained. However, the existing results are not applicable to the situation where the objects or attributes in a multi-scale decision table are sequentially updated, although this situation is frequently encountered in many real-world problems. Motivated by the fact that sequential three-way decisions are an effective mathematical tool in dealing with the data with information sequentially updated, we therefore use this methodology to investigate the optimal scale selection problem in a dynamic multi-scale decision table. Specifically, a sequential three-way decision model is first developed in multi-scale information tables, which can be viewed as multi-granularity of the universe of discourse. Then, this model is employed to present an optimal scale selection approach for such multi-scale decision tables that the number of objects is increasing. Finally, numerical experiments are conducted to evaluate the performance of the proposed optimal scale selection approach. Compared to the existing methods, the current approach does not need to consider the consistent and the inconsistent multi-scale decision tables separately and is especially suitable for updating the optimal scales of the multi-scale decision tables with new objects added.