Type-2 fuzzy logic systems have extensively been applied to various engineering problems, e.g. identification, prediction, control, pattern recognition, etc. in the past two decades, and the results were promising especially in the presence of significant uncertainties in the system. In the design of type-2 fuzzy logic systems, the early applications were realized in a way that both the antecedent and consequent parameters were chosen by the designer with perhaps some inputs from some experts. Since 2000s, a huge number of papers have been published which are based on the adaptation of the parameters of type-2 fuzzy logic systems using the training data either online or offline. Consequently, the major challenge was to design these systems in an optimal way in terms of their optimal structure and their corresponding optimal parameter update rules. In this review, the state of the art of the three major classes of optimization methods are investigated: derivative-based (computational approaches), derivative-free (heuristic methods) and hybrid methods which are the fusion of both the derivative-free and derivative-based methods. 
Optimal design of adaptive type-2 neuro-fuzzy systems: A review