Fuzzy ARTMAP (FAM) is a neural network model based on the adaptive resonance theory (ART). Its main advantage relies on its capability to successfully deal with the stability-plasticity dilemma. Even though FAM models have been used in many applications with remarkable performance, such model suffers from a well-known problem, named category proliferation, which results in the creation of a large number of categories in the training step. In that case, the FAM model may present lower generalization capability for unseen data. In this work, we aim to handle the category proliferation problem by proposing a new model that modifies the vigilance criterion and the weight update rule to pursue the generation of a sparse set of categories. Our model named FAM with Area of Influence (FAM-AI) is compared to the original FAM and some proposed variants. We perform several computational experiments and verify that, in general, the proposed FAM-AI achieves higher accuracy with a lower number of categories.