How well Fuzzy ARTMAP approximates functions?

Fuzzy ART and Fuzzy ARTMAP models arise from the synergy between the Fuzzy Set Theory and the Adaptive Resonance paradigm (ART). In this work, the performance of these models and the use of Fuzzy ARTMAP for function approximation are studied. In a first analysis, a relationship between the model parameters and the features of the generated categories is established. In the second part, the connection between these categories and the capacity of prediction of the model is analytically described. Joining these two studies, the link between the parameters and the prediction error of the model is found, in the form of bounds for the prediction error depending on the model parameters and the characteristics of the data used in the learning. These results provide a quantitative description of the parameter influence on the architecture behavior, opening the use of Fuzzy ARTMAP as a model for the unknown dynamic system identification from input/output data. To illustrate the theoretical developments, several experiments have been carried out using different kinds of functions, which show the accuracy of the proposed bounds.