A new approach of optimal scale selection to multi-scale decision tables

As a special case of information table, multi-scale decision table can usually be observed in real-life world. In such table, objects may take different values under the same attribute measured at different scales. Based on inclusion relation of subsets of attributes and coarse relation of scales of attributes, multi-layered granulations and stratified rough set approximations in multi-scale decision tables are shown from the perspective of granular computing. Compared with a special case studied by Wu and Leung, the multi-scale decision tables of diverse attributes with different numbers of levels of scales are studied in this paper. Furthermore, complement model and lattice model are proposed to analyze the optimal scale selection for multi-scale decision tables. Correspondingly, algorithms of the two models are designed and some experiments are performed to testify feasibilities of these proposed algorithms and to make comparisons of the models.