Solving fuzzy regression equation and its approximation for random fuzzy variable and their application

In this paper, the problem of linear regression is studied for random fuzzy quantity U which has some statistical linear relationship with another random real variable T. First, we turn the problem of fuzzy number linear regression model into the problem of usual real linear regression models, introduce the conception of r-linear regression equation of random fuzzy number, and give two results on what conditions we can determine the fuzzy number coefficients of the random fuzzy quantity linear regression equation by using these real number coefficients of r-linear regression equations. Then, we give specific method and steps to determine the fuzzy number coefficients of the random fuzzy number linear regression equation from a set of statistic of random fuzzy quantity U and random real variable T. And then, for convenience of application, we propose conception of alpha-approximation fuzzy number regression equations of random fuzzy number U with respect to random real variable T through further discussion to the fuzzy coefficients of the random fuzzy number linear regression equation and obtain the specific expressions of membership functions of the fuzzy coefficients of the alpha-approximation fuzzy number regression equations. At last, we give the specific method of solving the alpha-approximation fuzzy number regression equation and use a specific example to show the application and rationality of the proposed method.