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To synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, a novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the stability analysis of the proposed control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded and the external disturbance on the synchronization error can be attenuated. The simulation example, to synchronize two non-identical Chua's chaotic circuits, is given to confirm validity and synchronization performance of the advocated design methodology.