Incremental approaches for optimal scale selection in dynamic multi-scale set-valued decision tables

Optimal scale selection is crucial for knowledge discovery in multi-scale decision tables (MDTs). Set-valued decision tables are the generalized versions of single-valued decision information systems and can also be the multi-scale property. Existing researches do not consider the optimal scale selection in a multi-scale set-valued decision table. To address this issue, we introduce the concept of multi-scale set-valued decision tables and study the optimal scale selection problem of multi-scale set-valued decision tables (MSDTs) when the objects are dynamically increased. Firstly, we propose an MSDT model under dominance relations and investigate its characteristics. Secondly, a sequential three-way decision model is established in MSDT. Through reasoning and analyzing the changing trends of the three-way decision at different scales, the optimal scale selection method based on the undetermined degree is proposed. Thirdly, with the increments of the objects in MSDT, we develop incremental algorithms to accelerate optimal scale selection. Finally, a series of comparative experiments on UCI datasets show that our incremental algorithms outperform the non-incremental algorithms in terms of computational complexity.