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

Authors:
Mojtaba Ahmadieh Khanesar;Erdal Kayacan;Mohammad Teshnehlab;Okyay Kaynak
Affiliations:
Faculty of Electrical Engineering, Control Department, K. N. Toosi University of Technology , Tehran, Iran;Department of Electrical and Electronics Engineering, Bogazici University, Istanbul, Turkey;Faculty of Electrical Engineering, Control Department, K. N. Toosi University of Technology, Tehran, Iran;Department of Electrical and Electronics Engineering, Bogazici University, Istanbul, Turkey
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
2011

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Abstract

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.