  In order to achieve faster and more robust convergence (especially under
noisy working environments), a sliding mode theory-based learning algorithm has
been proposed to tune both the premise and consequent parts of type-2 fuzzy
neural networks in this paper. Differently from recent studies, where sliding
mode control theory-based rules are proposed for only the consequent part of
the network, the developed algorithm applies fully sliding mode parameter
update rules for both the premise and consequent parts of the type-2 fuzzy
neural networks. In addition, the responsible parameter for sharing the
contributions of the lower and upper parts of the type-2 fuzzy membership
functions is also tuned. Moreover, the learning rate of the network is updated
during the online training. The stability of the proposed learning algorithm
has been proved by using an appropriate Lyapunov function. Several comparisons
have been realized and shown that the proposed algorithm has faster convergence
speed than the existing methods such as gradient-based and swarm
intelligence-based methods. Moreover, the proposed learning algorithm has a
closed form, and it is easier to implement than the other existing methods.
