系数为LR-型模糊数的模糊线性最小二乘回归

Fuzzy Linear Least-squares Regression with LR-type Fuzzy Coefficients

针对输入、输出以及系数为LR-型模糊数的情况,建立模糊线性回归模型,提出该模型的最小二乘估计以及模型性能评价方法。当输入、输出以及系数都退化为精确值时,该估计退化为经典的最小二乘估计。该方法不仅适用于三角模糊数,也适用于其它LR-型模糊数(如指数型模糊数)。数值模拟表明,该方法的拟合效果较好。

In this paper,a fuzzy linear regression model is conducted,in which all of the inputs,outputs and coefficients are LR-type fuzzy numbers. The least-squares estimation and the performance evaluation method of the model are proposed. Especially, when the inputs, outputs and coefficients are crisp data, the estimation will be classical least squares estimation. The method is not only fits for the trian gular fuzzy numbers used commonly, but also fits for other LR-type fuzzy number, such as exponential-type fuzzy numbers. The experimental results show that this method have good fitness.