A Mutually Recurrent Interval Type-2 Neural Fuzzy System (MRIT2NFS) With Self-Evolving Structure and Parameters

In this paper, a mutually recurrent interval type-2 neural fuzzy system (MRIT2NFS) is proposed for the identification of nonlinear and time-varying systems. The MRIT2NFS uses type-2 fuzzy sets in order to enhance noise tolerance of the system. In the MRIT2NFS, the antecedent part of each recurrent fuzzy rule is defined using interval type-2 fuzzy sets, and the consequent part is of the Takagi-Sugeno-Kang type with interval weights. The antecedent part of MRIT2NFS forms a local internal feedback and interaction loop by feeding the rule firing strength of each rule to others including itself. The consequent is a linear combination of exogenous input variables. The learning of MRIT2NFS starts with an empty rule base and all rules are learned online via structure and parameter learning. The structure learning of MRIT2NFS uses online type-2 fuzzy clustering. For parameter learning, the consequent part parameters are tuned by rule-ordered Kalman filter algorithm to reinforce parameter learning ability. The type-2 fuzzy sets in the antecedent and weights representing the mutual feedback are learned by the gradient descent algorithm. After the training, a weight-elimination scheme eliminates feedback connections that do not have much effect on the network behavior. This method can efficiently remove redundant recurrence and interaction weights. Finally, the MRIT2NFS is used for system identification under both noise-free and noisy environments. For this, we consider both time series prediction and nonlinear plant modeling. Compared with type-1 recurrent fuzzy neural networks, simulation results show that our approach produces smaller root-mean-squared errors using the same number of iterations.