A further study on optimal scale selection in dynamic multi-scale decision information systems based on sequential three-way decisions

The optimal scale selection is the key problem in the study of multi-scale decision information systems. Dynamic change is one of the main features of big data, and the amount of information will often increase sharply with the passing of time. As is well known, the issue of updating the optimal scale of a multi-scale decision information system has been becoming a challenging problem in recent years, and it indeed has important theoretical and practical research values. Note that adding multiple objects can be viewed as adding one object multiple times. So, it just needs to clarify the change laws of optimal scale under the case of adding one object. Although the existing work has considered this problem in terms of the sufficient condition of updating the optimal scale, the results seem to be inaccurate. In other words, both sufficient and necessary conditions are still missing. In this paper, using sequential three-way decisions, the sufficient and necessary conditions of updating the optimal scale of a multi-scale decision information system are developed for the addition of an object, which makes the theoretical study on updating the optimal scale more complete.