The Optimal Scale Selecting In Dynamic Multi-scale Decision Tables Based On Sequential Three-way Decisions

With the improving efficiency and performance of various data observation tools and experimental equipment,and the diversified increasing of data processing method in practical application,the data we obtained has present a generally dynamic phenomenon of continuous growth,constantly updating and refining.And with the constantly data updating and data refining,it will lead to the dynamic change of the original information granule and the knowledge structure,so the timeliness has become the key problem of knowledge acquisition in dynamic data environment.The sequential three-way decision method is proposed by Yao,which is based on the decision making process that from coarse granularity to fine granularity,and the core idea is transforming the delay decision in boundary region into the certainty decision in positive region and negative region with the constantly new information collection.Considering the dynamic characteristics of the cost of decision making in the loss function,Liu discusses the dynamic three-way decision method base on decision-theoretic rough sets.For the objects have different knowledge granularity at different scales,Wu puts forward the multi-scale information tables theory.Obviously,the multiscale information tables is just the process of constantly information updating and refining.However,in real life although the enough detailed information may be more clear when we come to understand something,the costs of collecting and processing the information are also great in some measure,even the useless information in vast mount of data will waste much cost.In this case,it is worthless to detail the information.Therefore,we introduce the dynamic three-way decisions into multi-scale information tables and discuss the related problem about optimal scale selecting by dynamic three-way decisions in multi-scale decision tables.As is well known,one of the important problems in the study of multi-scale decision tables is to select the optimal level of scale,often called as the optimal scale selection problem.However,the existing obtained results on this problem are not applicable for the kind of multi-scale decision tables with object or attribute updating which are often encountered in real-world applications.Note that sequential three-way decisions are an effective mathematical tool for dealing with the data with information updating.So,in this paper,we use sequential three-way decisions to discuss the optimal scale selection problem for dynamic multi-scale decision tables.More specifically,a sequential three-way decisions model is first developed in multi-scale information tables,which can be viewed as multiple granularities of the universe of discourse.Then,selecting an optimal level of scale is investigated in multi-scale decision tables with object updating.Some interesting results are obtained,including that the changes on three-way decisions and optimal level of scale are clarified when object updating happens.Moreover,numerical experiments are conducted to evaluate the performance of the proposed optimal scale selection method.