Embedding HILK in a three-objective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers

HILK (Highly Interpretable Linguistic Knowledge) is a fuzzy modeling methodology especially thought for designing interpretable fuzzy rule-based systems. As starting point, it trusts on a domain expert able to define the most influential variables along with the most suitable number of linguistic terms for each of them. However, such task is not easy because problems often involve too many variables. To tackle with this problem, present paper proposes embedding HILK in a three-objective evolutionary algorithm (HILKMO) with the aim of making genetic feature selection and fuzzy partition learning. The use of two-objective (maximizing accuracy and interpretability) evolutionary algorithm has become very popular and effective when dealing with modeling interpretable fuzzy systems. There are also works dealing with three objectives but two of them are usually related to interpretability regarding only the readability of the system description. We have already emphasized, in previous works, the importance of addressing also the system comprehensibility. Therefore, the main contribution of this work is introducing two contradictory goals for characterizing interpretability: maximizing readability of the system explanation. The former objective prefers rules as compact as possible, while the latter one favors the use of rules with low interaction among them because rule interaction is difficult to explain. Both objectives are contradictory because the more compact the rule base, the higher the chance of having rules simultaneously fired by the same input vector. We have chosen NSGA-II as multi-objective evolutionary algorithm and our proposal is tested in the well-known GLASS benchmark problem.