TYPE-4 fuzzy clustering for fuzzy modeling applications

Abstract

In this study, a novel approach is described to the design of an interval type- 2 fuzzy neural system (IT2 FNS). It differs from the classical IT2 FNS in its use of parameterized conjunctors. In the optimization of the IT2 FNS, the membership functions are kept fixed and only the parameters of the conjunctors and the parameters in the consequent are tuned. In this study, the gradient based learning algorithm is used. The approach is tested for the modeling of a benchmark nonlinear function and for the wheel slip control of a quarter car model (QCM). In the stated applications, in the absence of any expert knowledge, some knowledge about the system is gained by the use of the interval type-2 fuzzy c-means (IT2 FCM) clustering algorithm. However, this requires the number of classes to be known beforehand. To alleviate this problem, some validity indices that have been suggested in the literature and a novel validity index that carries less computational burden are considered to determine the number of classes and the number of fuzzy rules. Another contribution to the existing literature is that in the design of an IT2 FNS, recursive FCM clustering algorithm is used and the designed algorithm is applied in control applications. The center and the standard deviation values of the interval type-2 Gaussian membership functions at the antecedent part of the Takagi-Sugeno-Kang type fuzzy rules are determined by the use of the recursive FCM clustering algorithm. The parameters at the consequent parts are tuned based on the gradient descent approach. The effectiveness of the designed algorithm is tested by simulation studies on a 2-DOF helicopter system and by experimental studies on a real-time servo system. The performance of the proposed method is compared with a traditional neuro-fuzzy structure adopted from the literature. In addition, IT2 FNS with recursive fuzzy c-means clustering is used with elliptical membership functions.