系数为非对称指数型模糊数的多元线性最小二乘回归

Multidimensional least-squares regression using asymmetric exponential fuzzy coefficients

使用模糊数之间的某种距离和的最小二乘方法 ,研究了模糊多元线性回归模型 ,此模型的输入为精确数据 ,输出为模糊数据 ,回归系数为非对称指数型模糊数 ,并通过讨论一元模糊线性回归模型 ,推导出三组正规方程组以分别用于求解模糊回归系数的模糊中心参数、左边参数和右边参数 ,然后将此结果推广到多元情形 。

The aim of this paper is to deal with the question of fuzzy multivariable linear regression with crisp input, fuzzy output data and asymmetric exponential fuzzy number coefficients. The method uses the distance of fuzzy numbers and the well-accepted least-squares fitting criterion.Firstly, a bivariate regression model using asymmetrical exponential fuzzy variables is derived. Three sets of mormal equations are formulated to solve the three parts of fuzzy regression coefficients: fuzzy center parameter, left parameter and right parameter respectively. Then, the method is extended to multiple regression analysis and the goodness of fit between the observed value and the estimated value is evaluated. Lastly a numerical example is used to demonstrate the proposed method.