We introduce a new fuzzy ARTMAP (FAM) neural network: Fuzzy ARTMAP with relevance factor (FAMR). The FAMR architecture is able to incrementally "grow" and to sequentially accommodate input-output sample pairs. Each training pair has a relevance factor assigned to it, proportional to the importance of that pair during the learning phase. The relevance factors are user-defined or computed. The FAMR can be trained as a classifier and, at the same time, as a nonparametric estimator of the probability that an input belongs to a given class. The FAMR probability estimation converges almost surely and in the mean square to the posterior probability. Our theoretical results also characterize the convergence rate of the approximation. Using a relevance factor adds more flexibility to the training phase, allowing ranking of sample pairs according to the confidence we have in the information source. We analyze the FAMR capability for mapping noisy functions when training data originates from multiple sources with known levels of noise.