Parameter identification of TSK neuro-fuzzy models

In the framework of the TSK neuro-fuzzy model a combination of the two well-known identification methods are employed for parameter estimation of the neuro-fuzzy inference system, namely the series–parallel and the parallel configurations. The presented paper proposes two new possible configurations for identifying the parameters of the TSK neuro-fuzzy model using the combinations of these two existing configurations. One of the proposed configurations constitutes the series–parallel configuration to the premise part and the parallel configuration to the consequent part of the neuro-fuzzy model, termed as PS-P configuration. The second one is composed of the series–parallel configuration to the consequent part and the parallel configuration to the premise part of the neuro-fuzzy model, termed as CS-P configuration. The presented work mainly deals with a comparative study of the proposed configurations and the existing configurations in the context of parameter identification of the TSK neuro-fuzzy model on three different benchmark examples. Moreover, it investigates upper bound of the learning rates, using the Lyapunov stability theorem, to assure the stability and the convergence of the model learning process. Implementation of the modified mountain clustering (MMC) and the cluster validity function yields initial models. To restrict the upper bound during the learning process it also presents a two-phase adaptive learning rate.