基于神经网络的模糊半参数回归模型

Fuzzy Semi-Parametric Regression Model Based on Neural Networks

摘要: 本文把样条基和BP (Back Propagation)神经网络的基本原理结合起来，从而提出了一种具有模糊输入和模糊输出的自适应模糊半参数回归模型。对于所提出的自适应模糊回归模型较好地解释了模型的内在依赖性和模糊性。文中借助截断幂基作为模型的一部分，然后与非参数部分结合构造半参回归模型。利用BP神经网络预测模型中的观测输出值，然后利用LR-型模糊数的交叉验证准则和基于绝对偏差的距离测度。通过求解光滑函数、光滑函数的光滑参数带宽和回归模型的未知系数，实现了构造自适应模糊半参数回归的目标函数优化问题。通过实例并计算模型的拟合度表明所提出的模型的有效性，该策略也显著提高了所提出算法的拟合优度，并为模糊回归模型提供了数值不确定性之间的依赖框架。

Abstract: In this paper, based on spline basis and BP (Back Propagation) neural network, an adaptive fuzzy semi-parametric regression model with fuzzy input and fuzzy output is presented. The intrinsic dependence and fuzziness of the adaptive fuzzy regression model are explained well. In this paper, the truncated spline basis is used as a part of the model, and then combined with the non-parametric part to construct a semi-parametric regression model. The BP neural network is used to predict the observed output values in the model, and then the cross validation criterion of LR-type fuzzy numbers and the distance measure based on absolute deviation are used. By solving the smooth function, the smooth parameter bandwidth of the smooth function and the unknown coefficient of the regression model, the objective function optimization problem of constructing adaptive fuzzy semi-parametric regression is realized. The effectiveness of the proposed model is demonstrated by an example and the fitting degree of the model is calculated. The proposed strategy also significantly improves the goodness of fit of the proposed algorithm, and provides a dependency framework for the fuzzy regression model between the numerical uncertainties.