基于结构元最小二乘序的模糊线性回归

Least-squares Order in Fuzzy Linear Regression Analysis Based on Structured Element

在具有模糊观测数据的线性回归问题中,通过定义模糊序指标实现模糊数的排序,借助经典最小二乘法原理,给出了使平方误差和在此排序方法下达到最小的模糊回归系数最小二乘序估计方法。三个例子的结果表明,文中的最小二乘方法能很好的对输入和输出为模糊数,回归系数为精确值的回归模型进行估计,更重要的是,此方法不仅对三角模糊数适用,对其他类型的模糊观测数据也适用。

In linear regression model with the fuzzy observations, ranking fuzzy number is proposed based on the defination of fuzzy order index. In this paper an idea stemmed from the classical least squares approach, the least squares order estimate is proposed for the fuzzy regression parameters, which the fuzzy sum of squared errors can be minimized under the method for ranking fuzzy numbers. The results of three cases show that the least-squares method of this paper is able to estimate well to the fuzzy regression model for fuzzy input-output data and the crisp regression coefficients. Most important, it works for all types of fuzzy obsevations, not restricted to the triangular one.