Journal paper
Journal papers accepted COAM, IJAR
15/06/26/10:18
L. Antoni, O. Krídlo, D. Kotlárová, D. López-Rodríguez and M. Ojeda-Aciego. Effective Greedy Boolean Matrix Factorization via the Rice-Siff Algorithm. Int. J of Approximate Reasoning 109747, 2026. In press
ABSTRACT This paper introduces a new Boolean Matrix Factorization (BMF) algorithm based on the Rice-Siff agglomerative clustering method. Our approach, Rice-Siff Factorization (RSF), integrates a greedy set-cover framework, where formal concepts serve as interpretable factors, with a dynamic candidate-generation process. By incorporating optimized variants such as RSF with Early Stopping (RSF-ES), we propose a pruning criterion based on order-theoretic properties to detect redundant candidates and significantly enhance factor extraction. Extensive synthetic benchmarks and experiments on real-world datasets demonstrate the effectiveness and robustness of the proposed framework, showing that RSF-ES provides significant scalability gains, yielding speedups on high-dimensional datasets with thousands of attributes while maintaining mathematical exactness. A comprehensive comparison with established factorization algorithms and an analysis of its theoretical properties show that RSF-ES represents a highly efficient and scalable solution for Boolean data analysis.
M. Ojeda-Hernández, D. López-Rodríguez. Direct-optimal systems of attribute implications in fuzzy formal concept analysis. Computational and Applied Mathematics 45:433, 2026
ABSTRACT Efficient closure computation is a key challenge in fuzzy Formal Concept Analysis. Direct implicational systems, which allow for one-step closure calculation, offer a powerful solution, but their formalization and practical computation in the fuzzy setting have remained largely open problems. This paper provides a comprehensive contribution to fill this gap. We first extend the concept of a direct system to fuzzy attribute implications and establish a complete theoretical characterization via a novel Fuzzy Exchange Condition. Building on this, we define the notion of a direct-optimal system and develop the DirectOptimal algorithm, a provably correct, interleaved strategy for its computation. A rigorous experimental evaluation demonstrates that our proposed algorithm is orders of magnitude more efficient than naive sequential approaches, and we diagnose the distinct computational bottlenecks that cause these simpler methods to fail. This work thus delivers a complete and empirically validated pipeline, from theory to practice, for the efficient computation of direct-optimal bases..
ABSTRACT This paper introduces a new Boolean Matrix Factorization (BMF) algorithm based on the Rice-Siff agglomerative clustering method. Our approach, Rice-Siff Factorization (RSF), integrates a greedy set-cover framework, where formal concepts serve as interpretable factors, with a dynamic candidate-generation process. By incorporating optimized variants such as RSF with Early Stopping (RSF-ES), we propose a pruning criterion based on order-theoretic properties to detect redundant candidates and significantly enhance factor extraction. Extensive synthetic benchmarks and experiments on real-world datasets demonstrate the effectiveness and robustness of the proposed framework, showing that RSF-ES provides significant scalability gains, yielding speedups on high-dimensional datasets with thousands of attributes while maintaining mathematical exactness. A comprehensive comparison with established factorization algorithms and an analysis of its theoretical properties show that RSF-ES represents a highly efficient and scalable solution for Boolean data analysis.
M. Ojeda-Hernández, D. López-Rodríguez. Direct-optimal systems of attribute implications in fuzzy formal concept analysis. Computational and Applied Mathematics 45:433, 2026
ABSTRACT Efficient closure computation is a key challenge in fuzzy Formal Concept Analysis. Direct implicational systems, which allow for one-step closure calculation, offer a powerful solution, but their formalization and practical computation in the fuzzy setting have remained largely open problems. This paper provides a comprehensive contribution to fill this gap. We first extend the concept of a direct system to fuzzy attribute implications and establish a complete theoretical characterization via a novel Fuzzy Exchange Condition. Building on this, we define the notion of a direct-optimal system and develop the DirectOptimal algorithm, a provably correct, interleaved strategy for its computation. A rigorous experimental evaluation demonstrates that our proposed algorithm is orders of magnitude more efficient than naive sequential approaches, and we diagnose the distinct computational bottlenecks that cause these simpler methods to fail. This work thus delivers a complete and empirically validated pipeline, from theory to practice, for the efficient computation of direct-optimal bases..
Journal papers accepted: INS
01/06/26/11:36
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, M. Ojeda-Aciego, B. De Baets. Fuzzy relational Galois connections: the final frontier. Information Sciences 754:123686, 2026.
ABSTRACT This work extends our research on fuzzy relational Galois connections, previously established in the context of complete Heyting algebras, to the broader framework of arbitrary residuated lattices. In this context, we study the properties of fuzzy closure relations and fuzzy closure systems, and the relationship with fuzzy relational Galois connections. The main result of the paper is the generalization of the necessary and sufficient conditions for the existence of a right adjoint for a fuzzy relation linking a fuzzy transitive directed graph to an unstructured set.
ABSTRACT This work extends our research on fuzzy relational Galois connections, previously established in the context of complete Heyting algebras, to the broader framework of arbitrary residuated lattices. In this context, we study the properties of fuzzy closure relations and fuzzy closure systems, and the relationship with fuzzy relational Galois connections. The main result of the paper is the generalization of the necessary and sufficient conditions for the existence of a right adjoint for a fuzzy relation linking a fuzzy transitive directed graph to an unstructured set.
Journal papers accepted FSS, INF
14/04/26/10:01
R. Belohlavek and M. Ojeda-Hernández. On monotony of fuzzy closure. Fuzzy Sets and Systems 109849, 2026
ABSTRACT Closure operators and systems play a significant role in a variety of areas of fuzzy logic. While the condition of monotony for ordinary closure operators has a straightforward form, two basic conditions of monotony naturally arise from the existing examples in a fuzzy setting. To unify these two conditions, two approaches can be found in the literature, one based on the notion of a filter of truth degrees and the other on the notion of a linguistic hedge. We present results connecting these approaches, explore their variants, and provide a notion of monotony that subsumes both the filter-based and hedge-based approaches. We study properties of this general concept of monotony and discuss open problems along with topics for future research.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Characterising quasi-closed elements via closure systems on complete fuzzy lattices. Informatica, 2026 (to appear)
ABSTRACT The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions..
ABSTRACT Closure operators and systems play a significant role in a variety of areas of fuzzy logic. While the condition of monotony for ordinary closure operators has a straightforward form, two basic conditions of monotony naturally arise from the existing examples in a fuzzy setting. To unify these two conditions, two approaches can be found in the literature, one based on the notion of a filter of truth degrees and the other on the notion of a linguistic hedge. We present results connecting these approaches, explore their variants, and provide a notion of monotony that subsumes both the filter-based and hedge-based approaches. We study properties of this general concept of monotony and discuss open problems along with topics for future research.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Characterising quasi-closed elements via closure systems on complete fuzzy lattices. Informatica, 2026 (to appear)
ABSTRACT The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions..
Journal paper accepted KBS
23/04/25/11:48
D. López, M. Ojeda-Hernández, T. Pattison. Systems of implications obtained using the Carve decomposition of a formal context. Knowledge-based systems, 318:113475, 2025.
ABSTRACT The Carve algorithm uses a divide-and-conquer strategy to compute the concept lattice of a formal context. The decomposition phase of the Carve algorithm discovers hierarchical structure in an amenable formal context, which the synthesis phase then exploits to construct the concept lattice from those of the component sub-contexts. In this paper, the problem of computing a sound and complete set of attribute implications via a refinement of the Carve decomposition is studied. Indeed, a set of rules is devised to obtain a set of valid implications which is proved to be complete. The refined decomposition and these rules are implemented in the novel Carve+ algorithm, whose runtime compares favorably with direct computation of the Duquenne–Guigues base of implications via the NextClosure algorithm.
ABSTRACT The Carve algorithm uses a divide-and-conquer strategy to compute the concept lattice of a formal context. The decomposition phase of the Carve algorithm discovers hierarchical structure in an amenable formal context, which the synthesis phase then exploits to construct the concept lattice from those of the component sub-contexts. In this paper, the problem of computing a sound and complete set of attribute implications via a refinement of the Carve decomposition is studied. Indeed, a set of rules is devised to obtain a set of valid implications which is proved to be complete. The refined decomposition and these rules are implemented in the novel Carve+ algorithm, whose runtime compares favorably with direct computation of the Duquenne–Guigues base of implications via the NextClosure algorithm.
Journal paper accepted: IJAR
10/03/25/10:26
H.J. Bello, M. Ojeda-Hernández, D. López-Rodríguez, C. Bejines. Fuzzy time series analysis: Expanding the scope with fuzzy numbers. Int. J. of Approximate Reasoning 180:Article 109387, 2025.
ABSTRACT This article delves into the process of fuzzifying time series, which entails converting a conventional time series into a time-indexed sequence of fuzzy numbers. The focus lies on the well-established practice of fuzzifying time series when a predefined degree of uncertainty is known, employing fuzzy numbers to quantify volatility or vagueness. To address practical challenges associated with volatility or vagueness quantification, we introduce the concept of informed time series. An algorithm is proposed to derive fuzzy time series, and findings include the examination of structural breaks within the realm of fuzzy time series. Additionally, this article underscores the significance of employing topological tools in the analysis of fuzzy time series, accentuating the role of these tools in extracting insights and unraveling intricate relationships within the data.
ABSTRACT This article delves into the process of fuzzifying time series, which entails converting a conventional time series into a time-indexed sequence of fuzzy numbers. The focus lies on the well-established practice of fuzzifying time series when a predefined degree of uncertainty is known, employing fuzzy numbers to quantify volatility or vagueness. To address practical challenges associated with volatility or vagueness quantification, we introduce the concept of informed time series. An algorithm is proposed to derive fuzzy time series, and findings include the examination of structural breaks within the realm of fuzzy time series. Additionally, this article underscores the significance of employing topological tools in the analysis of fuzzy time series, accentuating the role of these tools in extracting insights and unraveling intricate relationships within the data.
Journal paper accepted: IJAR
25/02/25/10:31
Francisco Pérez-Gámez, Carlos Bejines. An exploration of weak Heyting algebras: Characterization and properties. International Journal of Approximate Reasoning, 179: Article 109365, 2025.
ABSTRACT This paper explores weak Heyting algebras, an extension of complete Heyting algebras, focusing on characterizing this concept and identifying essential properties in terms of implication operators. The main emphasis is on unraveling the defining features and significance of the novel weak Heyting algebras. We further classify these structures within the context of a complete lattice and extend our findings to the Cartesian product. We facilitate comprehensive comparisons among these structures, by contributing to the broader understanding of weak Heyting algebras in mathematical research.
ABSTRACT This paper explores weak Heyting algebras, an extension of complete Heyting algebras, focusing on characterizing this concept and identifying essential properties in terms of implication operators. The main emphasis is on unraveling the defining features and significance of the novel weak Heyting algebras. We further classify these structures within the context of a complete lattice and extend our findings to the Cartesian product. We facilitate comprehensive comparisons among these structures, by contributing to the broader understanding of weak Heyting algebras in mathematical research.
Journal paper accepted: MMAS
05/02/25/13:34
N. Madrid and M. Ojeda-Aciego. On the φ-index of inclusion: studying the structure generated by a subset of indexes. Mathematical Methods in the Applied Sciences, 2025.
ABSTRACT The φ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the φ-index of inclusion, when its definition is restricted to a subset of indexes, are analyzed. The theoretical results obtained in this work are necessary in order to develop fuzzy inference systems based on the φ-index of inclusion.
ABSTRACT The φ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the φ-index of inclusion, when its definition is restricted to a subset of indexes, are analyzed. The theoretical results obtained in this work are necessary in order to develop fuzzy inference systems based on the φ-index of inclusion.
Journal paper accepted: NEUCOMP
07/01/25/12:00
I. Perfilieva, N. Madrid, M. Ojeda-Aciego, P. Artiemjew, A. Niemczynowicz. A Critical Analysis of the Theoretical Framework of the Extreme Learning Machine. Neurocomputing, 2025
ABSTRACT Despite several successful applications of the Extreme Learning Machine (ELM) as a new neural network training method that combines random selection with deterministic computation, we show that some fundamental principles of ELM lack a rigorous mathematical basis. In particular, we refute the proofs of two fundamental claims and construct datasets that serve as counterexamples to the ELM algorithm. Finally, we provide alternative claims to the basic principles that justify the effectiveness of ELM in some theoretical cases.
Journal paper accepted: Fuzzy Sets and Systems
02/11/23/10:36
M. Ojeda-Aciego, N. Madrid. Approaching the square of opposition in terms of the f-indexes of inclusion and contradiction. Fuzzy Sets and Systems.
ABSTRACT We continue our research line on the analysis of the properties of the f-indexes of inclusion and contradiction; in this paper, specifically, we show that both notions can be related by means of the, conveniently reformulated, Aristotelian square of opposition. We firstly show that the extreme cases of the f-indexes of inclusion and contradiction coincide with the vertexes of the Aristotelian square of opposition in the crisp case; then, we allocate the rest of f-indexes in the diagonals of the extreme cases and we prove that the Contradiction, Contrariety, Subcontrariety, Subalternation and Superalternation relations also hold between the f-indexes of inclusion and contradiction.
Journal paper accepted: Fuzzy Sets and Systems
04/10/23/12:41
M. Ojeda-Hernández, P. Cordero, I.P. Cabrera, E. Muñoz-Velasco. Fuzzy Closure Structures as Formal Concepts II. Fuzzy Sets and Systems.
ABSTRACT This paper is the natural extension of Fuzzy Closure Structures as Formal Concepts. In this paper we take into consideration the concept of closure system which is not dealt with in the previous one. Hence, a connection must be found between fuzzy ordered sets and a crisp ordered set. This problem is two-fold, the core of the fuzzy orders can be considered in order to complete the ensemble, or the crisp order can be fuzzified. Both ways are studied in the paper. The most interesting result is, similarly to the previous paper, that closure systems are formal concepts of these Galois connections as well.