arXiv subjects

Raquel Fernandez-Peralta

Publications and source records attributed to Raquel Fernandez-Peralta.

10 recordsLinked to original sources

arXiv2026

A lattice-theoretic framework for hesitant fuzzy convexity beyond scalar observables

In fuzzy-set theory, the notion of convexity has often been formulated through scalar reductions, typically via scores and aggregation functions. Although useful, such reductions may obscure relevant order-theoretic information in the codomain, especially in complex set-valued settings. This article develops a lattice-theoretic framework for convexity on lattice-valued mappings over point-convex segment-generated abstract convexity spaces. The framework separates the segment structure of the domain from the lattice structure of the codomain, distinguishing intrinsic convexity, defined through the lattice meet, from relational and observable convexities induced by preorders or scalar maps. The article characterizes when scalar observables preserve or reconstruct intrinsic convexity, and which codomain operators preserve it through their pointwise extensions. It then specializes the framework to hesitant fuzzy sets endowed with the symmetric lattice, recovering classical fuzzy and interval-valued convexities as natural restrictions. The structural result shows that the symmetric order cannot be represented by any finite family of scalar observables. This obstruction appears even on two-point typical hesitant fuzzy elements. Consequently, symmetric hesitant convexity cannot, in general, be reconstructed by any finite family of scalar observables. Moreover, every finite family of monotone scalar observables admits a three-point hesitant profile that is scalar-convex for all selected descriptions but not symmetrically convex.

math.GM↗

arXiv2026

Hypernetworks for Dynamic Feature Selection

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.

cs.LG↗

arXiv2026

Model-Agnostic Dynamic Feature Selection with Uncertainty Quantification

Dynamic feature selection (DFS) addresses budget constraints in decision-making by sequentially acquiring features for each instance, making it appealing for resource-limited scenarios. However, existing DFS methods require models specifically designed for the sequential acquisition setting, limiting compatibility with models already deployed in practice. Furthermore, they provide limited uncertainty quantification, undermining trust in high-stakes decisions. In this work, we show that DFS introduces new uncertainty sources compared to the static setting. We formalise how model adaptation to feature subsets induces epistemic uncertainty, how standard imputation strategies bias aleatoric uncertainty estimation, and why predictive confidence fails to discriminate between good and bad selection policies. We also propose a model-agnostic DFS framework compatible with pre-trained classifiers, including interpretable-by-design models, through efficient subset reparametrization strategies. Empirical evaluation on tabular and image datasets demonstrates competitive accuracy against state-of-the-art greedy and reinforcement learning-based DFS methods with both neural and rule-based classifiers. We further show that the identified uncertainty sources persist across most existing approaches, highlighting the need for uncertainty-aware DFS.

cs.LG↗

arXiv2025

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

cs.LG↗

arXiv2025

Fuzzy Implicative Rules: A Unified Approach

Rule mining algorithms are one of the fundamental techniques in data mining for disclosing significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rule to provide a solid theoretical framework for any fuzzy rule mining algorithm interested in capturing patterns in terms of logical conditionals rather than the co-occurrence of antecedent and consequent. In particular, we study which properties should satisfy the fuzzy operators to ensure a coherent behavior of different quality measures. As a consequence of this study, we introduce a new property of fuzzy implication functions related to a monotone behavior of the generalized modus ponens for which we provide different valid solutions. Also, we prove that our modeling generalizes others if an adequate choice of the fuzzy implication function is made, so it can be seen as an unifying framework. Further, we provide an open-source implementation in Python for mining fuzzy implicative associative rules. We test the applicability and relevance of our framework for different real datasets and fuzzy operators.

cs.LO↗

arXiv2025

Compact Rule-Based Classifier Learning via Gradient Descent

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.

cs.LG↗

arXiv2025

A global view of diverse construction methods of fuzzy implication functions rooted on F-chains

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.

cs.AI↗

arXiv2025

On the Non-Uniqueness of Representation of $(U,N)$-Implications

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.

cs.AI↗

arXiv2025

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.

cs.AI↗

arXiv2025

A Comprehensive Survey of Fuzzy Implication Functions

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.

cs.AI↗