模糊数据中异常点的一种识别方法  

Statistical Diagnostics of Fuzzy Linear Regression Model Based on Fuzzy Cook Distance

作　　者：张爱武[1] 

机构地区：[1]盐城师范学院数学科学学院,江苏盐城224002

出　　处：《工程数学学报》2012年第4期540-550,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071207;11171065);江苏省自然科学基金(2011058)~~

摘　　要：针对输入为确定数、输出为LR型模糊数的模糊数据集,利用最小二乘法建立了该模糊数据集的模糊线性回归分析模型及参数估计,用数据删除的方法研究了数据删除模糊线性回归模型,构造了统计诊断量—模糊Cook距离来识别模糊数据集中的异常点,通过数值模拟和对实例的研究,识别出其异常点,证实了本文构造的统计诊断量的有效性.Through utilizing the least squares method to construct the fuzzy linear regression analysis model and parameter estimation of the fuzzy data sets, whose input is definite number and output is LR type fuzzy number, and through using the data-delete method to learn data-delete fuzzy linear regression model, statistical diagnosis of the amount--fuzzy Cook distance is designed to identify the outliers existed in fuzzy data set. It is empirically verified that outliers can be effectively identified in the numerical simulation and the case study. It shows that the construction of the statistical diagnos- tics in the paper is valid.

关 键 词：模糊数据 异常点 模糊线性回归模型 数据删除模型 模糊Cook距离 

分 类 号：O212.4[理学—概率论与数理统计] O159[理学—数学]