Accurate, transparent and compact fuzzy models by multi-objective 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 multiobjective evolutionary algorithms are a suitable, because these are able to capture several non-dominated solutions in a single run of the algorithm. For fuzzy modeling, we describe two multi-objective evolutionary algorithms that consider all three objectives. Differences between both algorithms arise in the fuzzy sets considered, trapezoidal and gaussian respectively. The algorithms apply 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 algorithms. Finally, we propose a decision process to find the most satisfactory non-dominated solution. Results are shown for three approximation problems that were studied before by others authors.