Fuzzy nonparametric regression based on an adaptive neuro-fuzzy inference system

In this paper, a system, namely the adaptive neuro-fuzzy inference system (ANFIS), is investigated and used for fuzzy nonparametric regression function prediction with crisp input and fuzzy output. The fuzzy least squares problem based on Diamond׳s distance is proposed to optimize the consequent parameters in the hybrid algorithm of the adaptive neuro-fuzzy inference system method. Also, an algorithm is proposed to reduce bias and the boundary effect of the estimates of the underlying regression function. Various examples are used to illustrate and test the performance of this approach. The proposed method is compared with the local linear smoothing method for investigating the accuracy of the approach. The results demonstrate that the proposed method not only gives less biased estimates of the center line, the lower and the upper limit lines of underlying fuzzy regression function but also reduces bias and the boundary effect of the estimates of the underlying regression function by using the proposed algorithm significantly.