Comparison of Neural Networks with Different Membership Functions in the Type-2 Fuzzy Weights

Abstract

In this paper a comparison of the triangular, Gaussian, trapezoidal and generalized bell membership functions used in the type-2 fuzzy inference systems, which are applied to obtain the type-2 fuzzy weights in the connection between the layers of a neural network. We used two type-2 fuzzy systems that work in the backpropagation learning method with the type-2 fuzzy weight adjustment. We change the type of membership functions of the two type-2 fuzzy systems. The mathematical analysis of the proposed learning method architecture and the adaptation of the type-2 fuzzy weights are presented. The proposed method is based on recent methods that handle weight adaptation and especially fuzzy weights. In this work neural networks with type-2 fuzzy weights are presented. The proposed approach is applied to the case of Mackey-Glass time series prediction.KeywordsMembership FunctionNeural Network ArchitectureTime Series PredictionFuzzy WeightModular Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.