Journal paper accepted KBS
23/04/25/11:48 Filed in: Journal paper
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 Filed in: Journal paper
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 Filed in: Journal paper
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 Filed in: Journal paper
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 Filed in: Journal paper
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: MATHS
01/01/25/10:47 Filed in: Journal paper
D. López-Rodríguez, M. Ojeda-Hernández, and C. Bejines. New Simplification Rules for Databases with Positive and Negative Attributes. Mathematics 13.2 (2025). ABSTRACT In this paper, new logical equivalences are presented within the simplification logic with mixed attributes paradigm, which allow the obtention of bases of shorter, easier-to-read attribute implications. In addition to the theoretical results which show that the proposed equivalences indeed hold in simplification logic with mixed attributes, experimental results which showcase the effectiveness of this method are also provided. Furthermore, the simplification method presented is iterative and gives sufficiently good results in only one or two iterations, therefore presenting itself as a reasonable procedure in time-sensitive experiments.
Intl Seminar Participation
04/12/24/21:00 Filed in: seminar
M. Ojeda-Aciego. On the ƒ-index of inclusion: what is it? what is it good for? Seminar of AI of the Mathematical Institute of the Serbian Academy of Sciences and Arts .
We had the pleasure to participate at the Artificial Intelligence Seminar of the Mathematical Institute of the Serbian Academy of Sciences and Arts.
A number of interesting lines for further research were raised in the discussion following the presentation.
Thanks to Andreja Tepavcevic for the invitation.
ABSTRACT
The notion of inclusion is a cornerstone of set theory and therefore its generalisation in fuzzy set theory is of great interest. The functional degree (or φ-degree) of inclusion is defined to represent the degree of inclusion between two L-fuzzy sets in terms of a mapping that determines the minimal modifications required in one L-fuzzy set to be included in another in the sense of Zadeh. Thus, this notion differs from others existing in the literature because the φ-degree of inclusion is considered as a mapping instead of a value in the unit interval. We show that the φ-degree of inclusion satisfies versions of many common axioms usually required for inclusion measures in the literature.
Considering the relationship between fuzzy entropy and Young's axioms for measures of inclusion, we also present a measure of entropy based on the φ-degree of inclusion that is consistent with the axioms of De Luca and Termini. We then further study the properties of the φ-degree of inclusion and show that, given a fixed pair of fuzzy sets, their φ-degree of inclusion can be linked to a fuzzy conjunction that is part of an adjoint pair. We also show that when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair. Finally, we will focus on current work on the integration of the φ-degree of inclusion with FCA.
We had the pleasure to participate at the Artificial Intelligence Seminar of the Mathematical Institute of the Serbian Academy of Sciences and Arts.
A number of interesting lines for further research were raised in the discussion following the presentation.
Thanks to Andreja Tepavcevic for the invitation.
ABSTRACT
The notion of inclusion is a cornerstone of set theory and therefore its generalisation in fuzzy set theory is of great interest. The functional degree (or φ-degree) of inclusion is defined to represent the degree of inclusion between two L-fuzzy sets in terms of a mapping that determines the minimal modifications required in one L-fuzzy set to be included in another in the sense of Zadeh. Thus, this notion differs from others existing in the literature because the φ-degree of inclusion is considered as a mapping instead of a value in the unit interval. We show that the φ-degree of inclusion satisfies versions of many common axioms usually required for inclusion measures in the literature.
Considering the relationship between fuzzy entropy and Young's axioms for measures of inclusion, we also present a measure of entropy based on the φ-degree of inclusion that is consistent with the axioms of De Luca and Termini. We then further study the properties of the φ-degree of inclusion and show that, given a fixed pair of fuzzy sets, their φ-degree of inclusion can be linked to a fuzzy conjunction that is part of an adjoint pair. We also show that when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair. Finally, we will focus on current work on the integration of the φ-degree of inclusion with FCA.
CONCEPTS'24
14/09/24/11:49 Filed in: Conference participation
International Joint Conference on Conceptual Knowledge Structures 2024
Just back from CONCEPTS'24, the first joint event of the three main conferences on Formal Concept Analysis, namely, ICFCA, CLA and ICCS.
This first edition was held in Cadiz, in the Aulario La Bomba, an old barracks that is now used as a conference centre and exhibition hall by the University of Cadiz.
Our research team participated with seven communications.
- Nicolás Madrid presented Towards a generalized modus ponens based on the φ-index of inclusion.
- Domingo López-Rodríguez presented Rearrangement of fuzzy formal contexts for reducing cost of algorithms.
- Our external collaborator Ondrej Krídlo presented Connecting concept lattices with bonds between L-fuzzy formal contexts by external information.
- Our colleague Inma P. Cabrera presented Fuzzy relational Galois connections between fuzzy transitive digraphs, joint work with Emilio Muñoz-Velasco, Manuel Ojeda-Aciego and others.
- M. Ojeda-Hernández presented Obtaining the necessary concepts in a partial formal context.
- Carlos Bejines presented Aggregation of fuzzy graphs.
- Our colleague Fran Valverde presented Progress in Formal Context Transforms, joint work with Manuel Ojeda-Aciego and others.
IPMU'24
24/07/24/11:48 Filed in: Conference participation
Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems, IPMU 2024
Our last event before the summer holidays was the IPMU conference, held in Lisbon, Portugal, where we could meet a number of colleagues and, particularly, our external collaborators Bernard De Baets, Irina Perfilieva and Marek Reformat (who incidentally was also the Program Chair of the conference).
The next steps on our research line on Galois connections were discussed with Bernard, and further work on fuzzy mathematical morphology and the F-transform was discussed with Irina. The details of a draft to be submitted for publication were also discussed with Marek.
Our group presented four papers in the conference
- Manuel Ojeda-Hernandez, Domingo López-Rodríguez, Francisco Pérez-Gámez and Carlos Bejines López. Quasi and pseudo-closed elements in partial formal concept analysis
- Manuel Ojeda-Hernandez, Inma P. Cabrera, Pablo Cordero and Emilio Muñoz-Velasco. Fuzzy pseudointents
- Nicolas Madrid and Eloisa Ramírez Poussa. Analysis of the f-index of inclusion restricted to a set of indexes
- Michal Holcapek, Nhung Cao, Radek Valasek, Nicolas Madrid, Tomas Tichy and David Nedela. An Exploration of The Weighted Quantile Approach in Probabilistic Fuzzy Inference
