Update of optimal scale in dynamic multi-scale decision information systems

The problem of optimal scale selection for multi-scale decision information systems is an important issue in the field of granular computing research, especially when data are dynamically updated. Determining the changes of the optimal scale for dynamic data is a goal that has drawn increasing attention from scholars in related fields. For the case of object updating, solving this problem requires finding which characteristic conditions should be satisfied by newly added objects when different cases of the optimal scale occur. However, existing studies only include the sufficient and necessary condition of the optimal scale becoming smaller for dynamically updating objects. Therefore, to complete the theory regarding how the optimal scale will be changed when objects are dynamically updated, it is still necessary to explore the sufficient and necessary conditions for the optimal scale being unchanged or becoming larger. In this paper, we use three-way decision theory to study this problem. Concretely speaking, the uncertain region of three-way decision is used to reveal the change of knowledge at different scales. That is, the obtained results, combined with existing work, provide a nice solution to the problem of finding the changing laws of the optimal scale for object updating in multi-scale decision information systems.