一种新的基于样条函数的自适应模糊回归模型

A New Adaptive Fuzzy Regression Model Based on Spline Function

摘要: 本文对经典的模糊半参数部分线性模型进行了推广。在本文中，考虑将样条函数和非参方法结合起来进而应用在具有模糊解释变量和模糊响应变量的数据中来，并将模糊响应变量的展形作为模糊响应变量的中心的线性组合，从而构建出一种新的自适应模糊半参数回归模型。模型中重点考虑解释变量的中心与响应变量之间的关系，以简便所构造的模型。然后，提出了一种交叉验证和最小绝对偏差混合的方法来实现所构造的自适应模糊半参数回归的目标函数优化问题，进而估计模糊半参回归模型的非参数部分的带宽和参数部分中待估计的实系数。为了验证所提出模型的有效性，本文中利用了一些常用的拟合指标来检验回归模型的性能。最后将本文中提出的回归模型与所提出的方法进行了对比分析，结果表明所提出的回归模型是较为有效的和准确的。

Abstract: In this paper, the classical fuzzy semi-parametric partially linear model is extended. A new adaptive fuzzy semi-parametric regression model is constructed by combining spline function and nonpara-metric method in the data with fuzzy explanatory variable and fuzzy response variable, and taking the spread of fuzzy response variable as the linear combination of the center of fuzzy response var-iable. The model focuses on the relationship between the center of the explanatory variable and the response variable to simplify the constructed model. Then, a hybrid method of cross validation and minimum absolute deviation is proposed to optimize the objective function of the constructed adaptive fuzzy semi-parametric regression, and then the bandwidth of the non- parametric part of the fuzzy semi-parametric regression model and the real coefficients to be estimated in the para-metric part are estimated. In order to verify the validity of the proposed model, some commonly used fitting indexes are used to test the performance of the regression model. Finally, the regres-sion model proposed in this paper is compared with the proposed method, and the results show that the proposed regression model is more effective and accurate.