Exploiting fuzzy ordering relations to preserve interpretability in context adaptation of fuzzy systems

In the framework of context adaptation of fuzzy systems, a typical requirement of a contextualized system is to maintain the same interpretability as the original one. Here, we propose a novel index based on a fuzzy ordering relation to provide a measure of interpretability. Our index assesses ordering, distinguishability and coverage at the same time. We use the proposed index and the mean square error as goals of a multi-objective genetic algorithm aimed at generating contextualized Mamdani fuzzy systems with different trade-offs between the two goals. Results obtained on a synthetic data set are also discussed.