In this paper, a new learning algorithm for the Simpson's fuzzy min-max neural network is presented. It overcomes some undesired properties of the Simpson's model: specifically, in it there are neither thresholds that bound the dimension of the hyperboxes nor sensitivity parameters. Our new algorithm improves the network performance: in fact, the classification result does not depend on the presentation order of the patterns in the training set, and at each step, the classification error in the training set cannot increase. The new neural model is particularly useful in classification problems as it is shown by comparison with some fuzzy neural nets cited in literature (Simpson's min-max model, fuzzy ARTMAP proposed by Carpenter, Grossberg et al. in 1992, adaptive fuzzy systems as introduced by Wang in his book) and the classical multilayer perceptron neural network with backpropagation learning algorithm. The tests were executed on three different classification problems: the first one with two-dimensional synthetic data, the second one with realistic data generated by a simulator to find anomalies in the cooling system of a blast furnace, and the third one with real data for industrial diagnosis. The experiments were made following some recent evaluation criteria known in literature and by using Microsoft Visual C++ development environment on personal computers.