A fuzzy functional linear regression model with functional predictors and fuzzy responses

A novel functional regression model was introduced in this research in which, the predictor is a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was also proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzy-valued function. The performance of the proposed method was examined by some common goodness-of-fit criteria. The efficiency of the proposed method was then evaluated through two numerical examples; a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data were converted to scalar ones.