基于广义最大熵的具有模糊输入输出的回归模型的参数估计  

Parameter Estimation of a Regression Model with Fuzzy Input and Output Based on Generalized Maximum Entropy

作　　者：刘晓庆 陆秋君[1] LIU Xiao-qing;LU Qiu-jun(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

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》2020年第3期34-47,共14页Fuzzy Systems and Mathematics

基　　金：上海市一流学科(系统科学)建设项目(XTKX2012);上海市重点学科项目(T0502);沪江基金资助项目(B14005)。

摘　　要：模糊回归是在模糊系统中建立因变量与一组自变量之间关系的重要工具,以评估模糊自变量如何影响模糊响应变量的过程。当系统中出现小样本或者非列满秩设计矩阵时,模糊最小二乘法可能得出偏误估计。本文基于文献[13]中的多元线性回归模型,利用广义最大熵方法,针对模糊输入模糊输出数据,给出线性回归模型的参数估计和算法步骤。当输入或输出数据退化为清晰值时,该估计退化为清晰输入模糊输出或者模糊输入清晰输出的回归模型参数估计。本文结合模拟数据和实例数据,将广义最大熵方法与模糊最小二乘方法、岭估计方法进行比较研究,结果显示广义最大熵方法的可行性和有效性。Fuzzy regression is an important tool to establish the relationship between dependent variables and a group of independent variables in a fuzzy system,which evaluates how fuzzy independent variables affect fuzzy response variables.When small samples or non-column full rank design matrix appear in the system,the fuzzy least square method may obtain error estimation.Based on the multiple linear regression model in literature[13],this paper uses the generalized maximum entropy method to give parameter estimation and algorithm steps of the linear regression model for fuzzy input and fuzzy output data.When the input or output data degenerate into clear values,the estimation degenerates into the regression model parameter estimation of fuzzy output with clear input or fuzzy input with clear output.In this paper,the generalized maximum entropy method is compared with fuzzy least square method and ridge estimation method,and the results show that the generalized maximum entropy method is feasible and effective.

关 键 词：广义最大熵 模糊/清晰输入数据 模糊/清晰输出数据 模糊回归模型 蒙特卡洛模拟 

分 类 号：O159[理学—数学]