基于效用误差的变精度粗糙集的逼近性能研究  

Study on the Approximation Performance of Variable Precision Rough Set Based on Utility Error

作　　者：李艳[1] 李坤燕 李法朝[1,2] 靳晨霞[2] LI Yan;LI Kunyan;LI Fachao;JIN Chenxia(School of Science,Hebei University of Science and Technology,Shijiazhuang 050018,China;School of Economics and Management,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]河北科技大学经济管理学院,河北石家庄050018

出　　处：《山西大学学报（自然科学版）》2023年第1期79-90,共12页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(72101082,71771078);河北省自然科学基金(F2021208011)。

摘　　要：变精度粗糙集是数据决策问题中的一种常用的数据处理工具,如何选择粗糙精度、获得逼近效果最佳的上(下)近似集是设计数据处理方法的核心问题。文章首先以数据处理过程中必须面对的“错找到”与“未找到”两种偏差的作用价值不同为背景,构建了一种包容偏差价值的效用误差度量模式(简记为UE),讨论了UE的基本性质,其次以单个集合为目标集分别讨论了其变精度上、下近似集的逼近性能,从而给出了基于UE的最佳上(下)近似集的具体形式以及最佳粗糙精度的取值范围,最后结合具体算例进一步分析了最佳上(下)近似集的特征。理论推导和算例分析表明,UE具有良好的可解释性与可行性,最佳上(下)近似集与粗糙精度的相关结果可以为构建包容偏差价值的数据处理方法提供理论支撑,同时为考虑不同集合间综合逼近性能奠定基础,因此该研究具有广泛的应用前景。As a data processing tool, variable precision rough set is often used in data decision-making problems. How to choose rough precision and how to obtain the best upper(lower) approximation set are often regarded as the core problems of design data processing methods. In the process of data processing, we must face two kinds of deviations: "misfound" and "not found", which are regarded as the background of this paper because of their different functions and values. Firstly, a utility error measurement model(abbreviated as UE) containing deviation value is constructed. The basic properties of UE are discussed. Secondly, the approximation performances of variable precision upper and lower approximation sets with a single set as the target set are discussed, respectively. The specific form of the best upper(lower) approximation set and the range of the best rough precision based on UE are given. Finally, the characteristics of the best upper(lower) approximation set are further analyzed with a specific example. Theoretical derivation and example analysis show that UE has good interpretability and feasibility, and the correlation results between the best upper(lower) approximation set and rough precision can be used as theoretical support for the construction of data processing methods containing deviation value, and the foundation for considering the comprehensive approximation performance among different sets is laid. Therefore, this UE has a wide application prospect.

关 键 词：粗糙集 粗糙精度 效用误差 最佳上(下)近似集 数据决策 

分 类 号：O232[理学—运筹学与控制论]