Estimation of parameters for two-stage mixed fuzzy linear regression models

Combining nonlinear programming and least squares method, this paper proposes a two-stage mixed fuzzy linear regression model based on distance criterion. In order to ensure that the error of fuzzy estimated value and fuzzy observation value can be reduced when the explanatory variable is a clear number, the fuzzy regression model has a fuzzy adjustment term in addition to the clear regression coefficient. Firstly, based on the distance criterion, a nonlinear programming model is established to obtain the regression coefficient of the explanatory variables, and the fuzzy adjustment term is obtained based on the distance criterion and the least square method. Compared with the existing methods that cannot determine the sign of the coefficient, the method can accurately determine the sign of the regression coefficient. Finally, it is verified that the model has smaller mean square error and higher reliability than other models through a large number of numerical experiments and practical examples.