CFNN: Correlated fuzzy neural network

In this paper, a new fuzzy neural network model with correlated fuzzy rules (CFNN) based on the Levenberg-Marquardt (LM) optimization method is proposed. The proposed method is a new fuzzy network structure that is presented to approximate nonlinear functions especially the functions with high correlation between input variables with less number of fuzzy rules. A multivariable Gaussian fuzzy membership function is introduced that can consider the correlation between input variables and consequently it can model non-separable relations for interactive variables. The LM optimization method is used to learn parameters of both premise and consequent parts of the fuzzy rules. The suggested algorithm is successfully applied to seven tested examples including static function approximation, time-series prediction, non-linear dynamic system identification and a real-world complex regression problem. According to test observations; it can approximate nonlinear functions better than the other past algorithms with more compact structure and less number of fuzzy rules.