Analysis of the Noise Reduction Property of Type-2 Fuzzy Logic Systems Using a Novel Type-2 Membership Function

• Published in: IEEE transactions on cybernetics 2011-10, Vol.41 (5), p.1395-1406
• Main Authors: Khanesar, M. A., Kayacan, E., Teshnehlab, M., Kaynak, O.
• Format: Article
• Language: English
• Subjects: Cybernetics; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Mathematical analysis; Mathematical models; Noise reduction; Noise reduction property; Studies; Tuning; type-2 fuzzy logic (FL) system (FLS) (T2FLS); type-2 fuzzy sets; Uncertainty
• ISSN: 1083-4419; 2168-2267; 1941-0492; 2168-2275
• DOI: 10.1109/TSMCB.2011.2148173

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.