We propose a novel technique for the design of radial basis function (RBF) neural networks (NNs). To select various RBF parameters, the class membership information of training samples is utilized to produce a new cluster classes. This allows us to control performance as desired and approximate Neyman-Pearson classification. We show that by properly choosing the desired output neuron levels, then the RBF hidden to output layer performs Fisher discrimination analysis, and the full system performs a nonlinear Fisher analysis. Data on an agricultural product inspection problem and on synthetic data confirm the effectiveness of these methods.