Exploiting a coevolutionary approach to concurrently select training instances and learn rule bases of Mamdani fuzzy systems

When applied to high dimensional datasets, multi-objective evolutionary learning (MOEL) of fuzzy rule-based systems suffers from high computational costs, mainly due to the fitness evaluation. To use a reduced training set (TS) in place of the overall TS could considerably lessen the required effort. How this reduction should be performed, especially in the context of regression, is still an open issue. In this paper, we propose to adopt a co-evolutionary approach. In the execution of the MOEL, periodically, a single-objective genetic algorithm (SOGA) evolves a population of reduced TSs. The SOGA aims to maximize a purposely-defined index which measures how much a reduced TS is representative of the overall TS in the context of the MOEL. We tested our approach on a real world high dimensional dataset. We show that the Pareto fronts generated by applying the MOEL with the overall and the reduced TSs are comparable, although the use of the reduced TS allows saving on average the 75% of the execution time.