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A novel growing-and-pruning (GP) approach is proposed, which optimizes the structure of a fuzzy neural network (FNN). This GP-FNN is based on radial basis function neurons, which have center and width vectors. The structure-learning phase and the parameter-training phase are performed concurrently. The structure-learning approach relies on the sensitivity analysis of the output. A set of fuzzy rules can be inserted or reduced during the learning process. The parameter-training algorithm is implemented using a supervised gradient decent method. The convergence of the GP-FNN-learning process is also discussed in this paper. The proposed method effectively generates a fuzzy neural model with a highly accurate and compact structure. Simulation results demonstrate that the proposed GP-FNN has a self-organizing ability, which can determine the structure and parameters of the FNN automatically. The algorithm performs better than some other existing self-organizing FNN algorithms.