一种基于指数型距离的稳健模糊线性回归

A Robust Fuzzy Linear Regression Based on the Exponential-type Distance

本文针对LR-型模糊数,定义了一个指数型距离函数,在此基础上提出了一种稳健模糊线性回归方法.该方法将回归参数的估计转化为一个无约束最优化问题,其稳健性取决于指数型距离函数中一个参数的选择.数值试验表明,当在0.1与0.3之间取值时,所得模型稳健性较好;当趋近于零时,由该方法求得的模糊回归参数将退化为Diamond等人提出的最小二乘估计.

An exponential-type distance for LR-type fuzzy number is defined, and a robust fuzzy linear regression based on which is proposed. This method converts the estimation of regression parameters to a problem of nonrestraint optimization. It＇s robustness relies on the selection of a parameter in the exponential-type distance function. The experimental results show that the model has a good robustness when is in the interval [ 0. 1,0.3 ], and the parameters resulted from this method will be the least squares estimation proposed by Diamond when limits to zero.