Crisp complexity of fuzzy classifiers

Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger traction outside of fuzzy venues, because users sometimes do not know about fuzzy and because fuzzy partitions are not so easy to interpret in some situations. In this work, we propose a methodology to reduce fuzzy rule-based classifiers to crisp rule-based classifiers. We study different possible crisp descriptions and implement an algorithm to obtain them. Also, we analyze the complexity of the resulting crisp classifiers. We believe that our results can help both fuzzy and non-fuzzy practitioners understand better the way in which fuzzy rule bases partition the feature space and how easily one system can be translated to another and vice versa. Our complexity metric can also help to choose between different fuzzy classifiers based on what the equivalent crisp partitions look like.