Lowe proposed that the kernel parameters of a radial basis function (RBF) neural network may first be fixed and the weights of the output layer can then be determined by pseudo-inverse. Jang, Sun, and Mizutani (p.342) pointed out that this type of two-step training methods can also be used in fuzzy neural networks (FNNs). By extensive computer simulations, we demonstrated that an FNN with randomly fixed membership function parameters (FNN-RM) has faster training and better generalization in comparison to the classical FNN. To provide a theoretical basis for the FNN-RM, we present an intuitive proof of the universal approximation ability of the FNN-RM in this paper, based on the orthogonal set theory proposed by Kaminski and Strumillo for RBF neural networks.
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