A fuzzy linear regression model with better explanatory power

Previous studies on fuzzy linear regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude, which is not suitable for general cases. This paper proposes a two-stage approach to construct the fuzzy linear regression model. In the first stage, the fuzzy observations are defuzzified so that the traditional least-squares method can be applied to find a crisp regression line showing the general trend of the data. In the second stage, the error term of the fuzzy regression model, which represents the fuzziness of the data in a general sense, is determined to give the regression model the best explanatory power for the data. The results from two examples, one with crisp data and the other with fuzzy data for the independent variable, indicate that the two-stage method proposed in this paper has better performance than the previous studies.