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An RBF neural network model with fuzzy triangular numbers as inputs is set up to solve fuzzy multi-attribute decision making (MADM) problems. The model can determine the weights of attributes automatically so that weights are more objectively and accurately distributed. In this model, decision maker's specific preferences are considered in the determination of weights. It is simple, and can give objective results while taking into decision maker's subjective intensions. A numerical example is given to illustrate the method.