模糊线性回归模型参数估计的一种稳健方法  

Robust Method of Parameter Estimation for Fuzzy Linear Regression Model

作　　者：卢佩[1] 陆秋君[1] 徐家路 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《模糊系统与数学》2015年第6期160-168,共9页Fuzzy Systems and Mathematics

基　　金：沪江基金资助项目(B14005);上海理工大学博士启动经费项目(1000341001)

摘　　要：针对模糊线性回归模型传统的参数估计抗差能力较弱,容易夸大异常点的影响,提出一种基于数据调整的稳健估计方法。考虑系统输入为清晰数、输出为对称模糊数的数据集,本文首先回顾模糊线性回归模型传统的参数估计方法,并给出传统方法下基于数据删除的模型的影响分析以及模型的拟合评价方法。然后结合传统的参数估计方法,通过逐步删除异常点,直至模型达到满意的拟合优度,由回归模型得到模糊输出估计值后,引入3σ原则和纠正比例函数,在对系统初始数据进行剔除或纠正后求出回归模型的参数估计。最后数据集上的实验及比较均证实了算法的有效性,做到识别出异常点的同时,兼顾参数估计的质量。The results derived by traditional parameter estimation methods would be seriously damaged when there are outliers in the data set due to lack of robustness, so a robust algorithm for fuzzy linear regression is proposed based on data adjustment. Considering the data set wlth crisp inputs and symmetric fuzzy output,firstly,we illustrate the traditional methods of parameter estimation for fuzzy linear regression model, next case deletion analysis and fitting evaluation index on the model are given. Then the estimated values of parameters are obtained after the deletion or correction of the original data by means of case deletion analysis while introducing 3a principle and correction proportion function. Finally, experimental results on the data sets demonstrate the validity of the proposed algorithm, combining the quality of parameter estimation with identifying outliers.

关 键 词：模糊线性回归模型 稳健 模糊数 参数估计 

分 类 号：O159[理学—数学]