Analysis of the noise reduction property of type-2 fuzzy logic systems using a novel type-2 membership function

In this paper, the noise reduction property of type-2 fuzzy logic (FL) systems (FLSs) (T2FLSs) that use a novel type-2 fuzzy membership function is studied. The proposed type-2 membership function has certain values on both ends of the support and the kernel and some uncertain values for the other values of the support. The parameter tuning rules of a T2FLS that uses such a membership function are derived using the gradient descend learning algorithm. There exist a number of papers in the literature that claim that the performance of T2FLSs is better than type-1 FLSs under noisy conditions, and the claim is tried to be justified by simulation studies only for some specific systems. In this paper, a simpler T2FLS is considered with the novel membership function proposed in which the effect of input noise in the rule base is shown numerically in a general way. The proposed type-2 fuzzy neuro structure is tested on different input-output data sets, and it is shown that the T2FLS with the proposed novel membership function has better noise reduction property when compared to the type-1 counterparts.