Fuzzy modeling with multi-objective neuro-evolutionary algorithms

Interpretability aspects of fuzzy models have received quite some attention in recent years and may be obtained by using transparent rule-structures and well characterized fuzzy membership functions. Moreover, model compactness is important for the interpretability and is related to the number of rules and fuzzy sets. Besides these two criteria, the model accuracy should always be taken into account. In this way, several criteria appear in fuzzy modeling and then multi-objective evolutionary algorithms are suitable to capture several nondominated solutions in a single run of the algorithm. For fuzzy modeling, we describe a multi-objective neuro-evolutionary algorithm that considers all three objectives. The algorithm applies an accuracy criterium and a transparency criterium, based on fuzzy set similarity, while compactness is achieved by a specific technique, incorporated ad hoc within the evolutionary algorithm. Results are shown for an approximation problem studied before by other authors.