分层多尺度决策信息系统的序贯三支决策

Sequential three-way decision of hierarchical multi-scale decision information system

传统信息系统中每个属性只有一个尺度,但随着海量数据的涌现,实际应用中经常是在多个尺度上处理和分析问题.三支决策是解决分类问题的一种经典方法,序贯三支决策是在三支决策的基础上进行多步决策的一种方法.将多尺度决策信息系统与三支决策相结合,基于决策理论粗糙集提出分层多尺度决策信息系统的序贯三支决策模型,得到动态变化的正域、负域、边界域.对多尺度决策信息系统进行分层,依次在分层后得到的多个单尺度决策信息系统上进行讨论,构建尺度层面的序贯结构;在每个单尺度决策信息系统上,通过增加属性的方式得到属性子集序列,诱导出多级粒度结构,构建该尺度下粒度层面的序贯结构.为此,给出两种属性子集序列的选择方法;在序贯三支决策过程中,利用相对损失函数计算阈值,并讨论了阈值的性质;最后给出序贯三支决策过程中的分类规则,并用实例说明提出的模型能有效地处理分类问题.

In traditional information systems,each attribute has only one scale,but with the emergence of massive data,we often deal with and analyze problems on multiple scales in practical applications.Three-way decision(3WD)is a classical method to solve the classification problem.Sequential three-way decision(S3WD)is a method of multi-step decision-making based on 3WD.This paper combines multi-scale decision information system with 3WD.Based on decision-theoretic rough sets(DTRSs),the sequential three-way decision model of hierarchical multi-scale decision information system is proposed.After that,the dynamic positive region,negative region and boundary region can be obtained.The multi-scale decision information system is layered.It is discussed in turn on multiple single-scale decision information systems obtained after stratification,and the sequential structure of the scale level is constructed.On each single-scale decision information system,the attribute subset sequence is obtained by adding attributes,and the multilevel granular structure is induced to construct the sequential structure at the granularity level.For this reason,this paper gives two selection methods for the collection of attribute subsets,and in the S3WD process,the relative loss function is used to calculate the threshold,and the properties of the threshold are discussed.Finally,the classification rules in the S3WD process are given,and an example is given to illustrate that the proposed model can effectively deal with the classification problem.