An Interval-Valued Fuzzy Cerebellar Model Neural Network Based on Intuitionistic Fuzzy Sets

Abstract

An interval-valued fuzzy cerebellar model neural network (IV-FCMNN) is proposed for the identification and control of uncertain systems. It is a more general model that uses the framework of a cerebellar model neural network (CMNN) and Atanassov intuitionistic fuzzy sets (AIFSs), so that the mathematical representation of a fuzzy event is more complete and the fuzzy neural network is more general. In some special cases, this neural network can be reduced to an interval-valued fuzzy neural network (IV-FNN), a fuzzy neural network (FNN), a fuzzy cerebellar model neural network (FCMNN) or a CMNN. Since the interval-type input data are used to realize this algorithm, the IV-FCMNN copes better with uncertainty and allows greater freedom of design. Therefore, the ability to learn, the approximation precision and the fuzzy semantic description of this network are much better than those of other models. In the proposed IV-FCMNN, a training algorithm that uses a gradient descent method is proposed to adjust the parameters and convergence is proved using the Lyapunov stability theorem. The variable learning rates are analyzed and the optimal learning rates are also determined. For demonstrating the effectiveness of the proposed IV-FCMNN, three types of applications, including multiple functions approximation, multi-dimensional classification and nonlinear dynamic system feedback control, are performed and the comparison with other models are also provided.