A new uncertain linear regression model based on equation deformation

被引：14
|
作者：
Wang, Shuai [1 ,2 ]
Ning, Yufu [1 ,2 ]
Shi, Hongmei [3 ]
机构：
[1] Shandong Youth Univ Polit Sci, Sch Informat Engn, 31699 Jingshi East Rd, Jinan, Peoples R China
[2] Key Lab Informat Secur & Intelligent Control Univ, Jinan 250100, Peoples R China
[3] Shandong Agr & Engn Univ, Sch Informat Sci & Engn, 866 Nongganyuan Rd, Jinan, Peoples R China
来源：
SOFT COMPUTING | 2021年 / 25卷 / 20期
基金：
中国国家自然科学基金;
关键词：
Equation deformation method; Least squares estimation; Linear regression model; Uncertainty theory;
D O I：
10.1007/s00500-021-06030-7
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linear regression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer's rule and matrix and propose the Cramer's rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation.
引用
收藏
页码：12817 / 12824
页数：8
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