Raquel Fernandez-Peralta

Javier Fumanal-Idocin, Raquel Fernandez-Peralta, Javier Andreu-Perez

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

Javier Fumanal-Idocin, Raquel Fernandez-Peralta, Javier Andreu-Perez

Dynamic feature selection (DFS) is a machine learning framework in which features are acquired sequentially for individual samples under budget constraints. The exponential growth in the number of possible feature acquisition paths forces a DFS model to balance fitting specific scenarios against maintaining general performance, even when the feature space is moderate in size. In this paper, we study the structural limitations of existing DFS approaches to achieve an optimal solution. Then, we propose \textsc{Hyper-DFS}, a hypernetwork-based DFS approach that generates feature subset-specific classifier parameters on demand. We show that the use of hypernetworks compared to mask-embedding methods results in a smaller structural complexity bound. We also use a Set Transformer encoding to create a smooth conditioning space for the hypernetwork, so that functionally similar tasks are also geometrically close. In our benchmarks, \textsc{Hyper-DFS} outperforms all state-of-the-art approaches on synthetic and real-life tabular data. It is also competitive or superior across all image datasets tested, and shows substantially stronger zero-shot generalisation to feature subsets never seen during training than existing DFS approaches.

Raquel Fernandez-Peralta

Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the last ten years many new families have been introduced, each defined by specific construction methods and having different key properties. This survey aims to provide a comprehensive and structured overview of the diverse families of fuzzy implication functions, emphasizing their motivations, properties, and potential applications. By organizing the information schematically, this document serves as a valuable resource for both theoretical researchers seeking to avoid redundancy and practitioners looking to select appropriate operators for specific applications.

Javier Fumanal-Idocin, Raquel Fernandez-Peralta, Javier Andreu-Perez

Rule-based models are essential for high-stakes decision-making due to their transparency and interpretability, but their discrete nature creates challenges for optimization and scalability. In this work, we present the Fuzzy Rule-based Reasoner (FRR), a novel gradient-based rule learning system that supports strict user constraints over rule-based complexity while achieving competitive performance. To maximize interpretability, the FRR uses semantically meaningful fuzzy logic partitions, unattainable with existing neuro-fuzzy approaches, and sufficient (single-rule) decision-making, which avoids the combinatorial complexity of additive rule ensembles. Through extensive evaluation across 40 datasets, FRR demonstrates: (1) superior performance to traditional rule-based methods (e.g., $5\%$ average accuracy over RIPPER); (2) comparable accuracy to tree-based models (e.g., CART) using rule bases $90\%$ more compact; and (3) achieves $96\%$ of the accuracy of state-of-the-art additive rule-based models while using only sufficient rules and requiring only $3\%$ of their rule base size.

Raquel Fernandez-Peralta, Andrea Mesiarová-Zemánková

Fuzzy implication functions constitute fundamental operators in fuzzy logic systems, extending classical conditionals to manage uncertainty in logical inference. Among the extensive families of these operators, generalizations of the classical material implication have received considerable theoretical attention, particularly $(S,N)$-implications constructed from t-conorms and fuzzy negations, and their further generalizations to $(U,N)$-implications using disjunctive uninorms. Prior work has established characterization theorems for these families under the assumption that the fuzzy negation $N$ is continuous, ensuring uniqueness of representation. In this paper, we disprove this last fact for $(U,N)$-implications and we show that they do not necessarily possess a unique representation, even if the fuzzy negation is continuous. Further, we provide a comprehensive study of uniqueness conditions for both uninorms with continuous and non-continuous underlying functions. Our results offer important theoretical insights into the structural properties of these operators.

Raquel Fernandez-Peralta, Juan Vicente Riera

Fuzzy implication functions are one of the most important operators used in the fuzzy logic framework. While their flexible definition allows for diverse families with distinct properties, this variety needs a deeper theoretical understanding of their structural relationships. In this work, we focus on the study of construction methods, which employ different techniques to generate new fuzzy implication functions from existing ones. Particularly, we generalize the $F$-chain-based construction, recently introduced by Mesiar et al. to extend a method for constructing aggregation functions to the context of fuzzy implication functions. Our generalization employs collections of fuzzy implication functions rather than single ones, and uses two different increasing functions instead of a unique $F$-chain. We analyze property preservation under this construction and establish sufficient conditions. Furthermore, we demonstrate that our generalized $F$-chain-based construction is a unifying framework for several existing methods. In particular, we show that various construction techniques, such as contraposition, aggregation, and generalized vertical/horizontal threshold methods, can be reformulated within our approach. This reveals structural similarities between seemingly distinct construction strategies and provides a cohesive perspective on fuzzy implication construction methods.

Javier Fumanal-Idocin, Raquel Fernandez-Peralta, Javier Andreu-Perez

Dynamic feature selection (DFS) offers a compelling alternative to traditional, static feature selection by adapting the selected features to each individual sample. Unlike classical methods that apply a uniform feature set, DFS customizes feature selection per sample, providing insight into the decision-making process for each case. DFS is especially significant in settings where decision transparency is key, i.e., clinical decisions; however, existing methods use opaque models, which hinder their applicability in real-life scenarios. This paper introduces a novel approach leveraging a rule-based system as a base classifier for the DFS process, which enhances decision interpretability compared to neural estimators. We also show how this method provides a quantitative measure of uncertainty for each feature query and can make the feature selection process computationally lighter by constraining the feature search space. We also discuss when greedy selection of conditional mutual information is equivalent to selecting features that minimize the difference with respect to the global model predictions. Finally, we demonstrate the competitive performance of our rule-based DFS approach against established and state-of-the-art greedy and RL methods, which are mostly considered opaque, compared to our explainable rule-based system.

Raquel Fernandez-Peralta, Javier Fumanal-Idocin, Javier Andreu-Perez

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.