Fuzzy spline univariate regression with exact predictors and fuzzy responses

Spline smoothing is a form of nonlinear regression when there is reason to believe that relationship between the predictor and the response is curvilinear. In such cases, the spline smoothing is an effective method to improve the performances of the conventional polynomial-based regression models. This paper proposed a fuzzy spline method based on a weighted absolute error distance measure with exact predictors and fuzzy responses. Unknown fuzzy coefficients, tuning parameter were selected according to a hybrid optimization algorithm. The effectiveness of the proposed method was also examined and compared with some well-established fuzzy nonlinear regression models through some numerical examples including a simulation study. For this purpose, several common goodness-of-fit criteria were employed. The numerical results clearly indicated that our prediction/estimation gives more accurate results compared to other methods.