Extension of fuzzy adaptive laws to IT2 fuzzy systems

As an extension of T1 FLS, IT2 FLS was proposed to handle a higher level of uncertainties by providing an additional dimension to FSs. This paper investigates IT2 FLSs´ advantages over type-1 FLSs in adaptive fuzzy systems. It is shown that the uncertainties existing in consequent sets could not be fully utilized when type-reduction is performed using the uncertainty bounds method, which may limit the potential advantages of adaptive IT2 fuzzy systems. To address this limitation, a type-reduction method based on two of the four boundary embedded type-1 FLSs in the uncertainty bounds method is proposed. Moreover, we also establish the condition when adaptive fuzzy systems using T1 FLSs and IT2 FLSs have the same performance. Lastly, IT2 FLSs using the proposed type-reduction method are demonstrated to have greater approximation ability than type-1 FLSs through numerical experiments.