Estimating the parameters of fuzzy linear regression model with crisp inputs and Gaussian fuzzy outputs: A goal programming approach

In this paper, we offered a new method to fit a fuzzy linear regression model to a set of crisp inputs and Gaussian fuzzy outputs, by considering its parameters as Gaussian fuzzy numbers. To calculate the regression coefficients, a nonlinear programming model is formulated based on a new distance between Gaussian fuzzy numbers. The nonlinear programming model is converted to a goal programming model by choosing appropriate deviation variables and then to a linear programming which can be solved simply by simplex method. To show the efficiency of proposed model, some applicative examples are solved and three simulation studies are performed. The computational results are compared with some earlier methods.