Interval type-2 fuzzy logic systems: theory and design

Abstract

This Ph.D. dissertation has four main objectives. Firstly, the noise reduction property of type-2 fuzzy logic systems that use a novel type-2 fuzzy membership function is studied. A number of papers exist in literature that claim the performance of type-2 fuzzy logic systems is better than that of type-1 fuzzy logic systems under noisy conditions, and this claim is supported by simulation studies only for some specific systems. In this dissertation, a simpler type-2 fuzzy logic system 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. Secondly, fuzzy c-means clustering algorithm is proposed for type-2 fuzzy logic systems to determine the initial places of the membership functions to ensure that the gradient descent algorithm used afterwards converges in a shorter time. Thirdly, Levenberg-Marquardt algorithm is proposed for type-2 fuzzy neural networks. While conventional gradient descent algorithms use only the first order derivative, the proposed algorithm used in this dissertation benefits from the first and the second-order derivatives which makes the training procedure faster. Finally, a novel sliding mode control theory-based learning algorithm is proposed to train the parameters of the type-2 fuzzy neural networks. In the approach, instead of trying to minimize an error function, the weights of the network are tuned by the proposed algorithm in a way that the error is enforced to satisfy a stable equation. The parameter update rules are derived for both Gaussian and triangular type-2 fuzzy membership functions, and the convergence of the weights is proven by Lyapunov stability method. The simulation results indicate that the type-2 fuzzy structure with the proposed learning algorithm results in a better performance than its type-1 fuzzy counterpart.