Optimal scale selection and attribute reduction in multi-scale decision tables based on three-way decision

Optimal scale selection and attribute reduction are two key issues related to knowledge discovery in multi-scale decision tables (MDTs). The former is mainly used to obtain optimal scale combinations by selecting a suitable scale for each attribute, while the latter attempts to obtain reducts of these optimal scale combinations (i.e., optimal scale reducts). However, a search for all optimal scale reducts of a given MDT may result in a combinatorial explosion and existing approaches typically incur excessive time consumption. In this paper, a novel scale combination is defined to perform optimal scale selection and attribute reduction synchronously. Accordingly, an effective approach integrating sequential three-way decision with simplified MDTs is proposed to search for all optimal scale reducts. The efficiency of searching can be significantly improved by reducing the number of consistency checks required for single-scale decision tables and accelerating each check. First, a sequential three-way decision model of the scale space is proposed to search for all optimal scale reducts. Based on the trisecting-and-acting concept and a multi-step strategy, a large number of non-optimal scale reducts can be progressively transferred from the boundary regions to the negative regions. Second, an extended stepwise optimal scale selection method is introduced to quickly search for a single optimal scale reduct in the boundary region. Finally, a simplified MDT is proposed to accelerate the consistency checks for single-scale decision tables. Accordingly, an optimal scale selection algorithm integrating sequential three-way decision with simplified MDTs is proposed to improve the efficiency of searching for all optimal scale reducts. Experimental results demonstrate that the proposed algorithm can significantly reduce overall computational time.