A Fast Interpretable Fuzzy Tree Learner

Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not guaranteed by many existing fuzzy rule-mining algorithms. Evolutionary approaches can produce high-quality models but suffer from prohibitive computational costs, while neural-based methods like ANFIS have problems retaining linguistic interpretations. In this work, we propose an adaptation of classical tree-based splitting algorithms from crisp rules to fuzzy trees, combining the computational efficiency of greedy algoritms with the interpretability advantages of fuzzy logic. This approach achieves interpretable linguistic partitions and substantially improves running time compared to evolutionary-based approaches while maintaining competitive predictive performance. Our experiments on tabular classification benchmarks proof that our method achieves comparable accuracy to state-of-the-art fuzzy classifiers with significantly lower computational cost and produces more interpretable rule bases with constrained complexity. Code is available in: https://github.com/Fuminides/fuzzy_greedy_tree_public

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.

Compact Rule-Based Classifier Learning via Gradient Descent

Rule-based models play a crucial role in scenarios that require transparency and accountable decision-making. However, they primarily consist of discrete parameters and structures, which presents challenges for scalability and optimization. In this work, we introduce a new rule-based classifier trained using gradient descent, in which the user can control the maximum number and length of the rules. For numerical partitions, the user can also control the partitions used with fuzzy sets, which also helps keep the number of partitions small. We perform a series of exhaustive experiments on $40$ datasets to show how this classifier performs in terms of accuracy and rule base size. Then, we compare our results with a genetic search that fits an equivalent classifier and with other explainable and non-explainable state-of-the-art classifiers. Our results show how our method can obtain compact rule bases that use significantly fewer patterns than other rule-based methods and perform better than other explainable classifiers.