A matrix method for estimating linear regression coefficients based on fuzzy numbers

Abstract

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression models, and then convert the two models into Ax = y, in which A is the linear regression coefficient and x is the independent variable and y variable It Depends, where A is the linear regression coefficient and x is independent variable and y is dependent variable. Finally, to minimize this device, we use the total sum of squared error based on distance d. In two examples, the proposed method is compared with the only available method.