Sliding mode incremental learning algorithm for interval type-2 Takagi-Sugeno-Kang fuzzy neural networks

Type-2 fuzzy logic systems are an area of growing interest over the last years. The ability to model uncertainties and to perform under noisy conditions in a better way than type-1 fuzzy logic systems increases their applicability. A new stable on-line learning algorithm for interval type-2 Takagi–Sugeno–Kang (TSK) fuzzy neural networks is proposed in this paper. Differently from the other recently proposed variable structure system theorybased on-line learning approaches for the type-2 TSK fuzzy neural nets, where the adopted consequent part of the fuzzy rules consists solely of a constant, the developed algorithm applies the complete structure of the Takagi–Sugeno type fuzzy if–then rule base (i.e. first order instead of zero order output function is implemented). In addition it is able to adapt the existing relation between the lower and the upper membership functions of the type-2 fuzzy systems. This allows managing of non-uniform uncertainties. Simulation results from the identification of a nonlinear system with uncertainties and a non-bounded-input bounded-output nonlinear plant with added output noise have demonstrated the better performance of the proposed algorithm in comparison with the previously reported in the literature sliding mode on-line learning algorithms for both type-1 and type-2 fuzzy neural structures.