Journal paper accepted MATHS
19/12/25/10:16 Filed in: Journal paper
F. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. Formal Context Transforms and their Affordances for Exploratory Data Analysis. Mathematics , 2025. To appear
ABSTRACT Consider a formal context (G, M, I) as the basic mechanism to capture information about a set G of objects, a set M of attributes and the relation I ∈ G × M between them. Traditional use of Formal Concept Analysis has some shortcomings in its information-eliciting capabilities, which were expanded by the related processes of Formal Independence Analysis and Formal Equivalence Analysis, which analyse different information types. The core of these three approaches can be seen as different instantiations of a theorem by Birkhoff when applied to different concept-forming operators (technically, some types of Galois connection). In this paper, we propose the notion of context transform as a way to elicit new information types from contexts that we call information qualia. We apply this notion of context transform to explain how we may expect other formal analyses of different information qualia to arise from a formal context. We also use the concept of formal quale across the board to provide the affordances of many of the choices needed for practitioners to make effective use of data analysis techniques.
Journal papers accepted FSS, COAM
28/11/25/10:00 Filed in: Journal papers
N. Madrid, M. Ojeda-Aciego. Composition as a fuzzy conjunction between indexes of inclusions. Fuzzy Sets and Systems, Article 109685, 2026.
ABSTRACT We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.
H. Bello, P. Jiménez, C. Bejines. Examining fuzzy number approximation through a topological algebraic approach. Computational and Applied Mathematics 45, 81 (2026).
ABSTRACT In this paper, we delve into the study of fuzzy number approximation by LR fuzzy numbers, shedding light on their algebraic properties. We present a solid approach to approximate fuzzy numbers keeping the same expected interval and core proving that such approximation is additive and continuous under a wide family of distances. As a key part of this construction, we study the set of fuzzy numbers as a topological monoid and develop a process to embed any cancellative abelian topological monoid with open shifts in a topological abelian group. This allows us to demonstrate a highly useful result in the context of this paper: the continuity of homomorphisms between cancellative topological abelian monoids with open shifts is equivalent to its continuity at zero.
D. López-Rodríguez, M. Ojeda-Hernández, A. Mora, C. Bejines. Close-by-One-like algorithms in the fuzzy setting: Theory and experimentation. Fuzzy Sets and Systems 520, Article 109574, 2025.
ABSTRACT In Fuzzy Formal Concept Analysis (FFCA), concept lattices are computed by scaling the problem and applying ordinary FCA algorithms. In this paper, the CbO family of algorithms is extended to work natively in the fuzzy setting, they are proved to be correct and output the whole set of formal concepts, which makes them mathematically equivalent to the scaling approach.
However, experimental results demonstrate the performance improvement of these methods compared to scaling. The paper also discusses a new fuzzy strategy based on blacklisting redundant truth values to enhance the performance of algorithms by taking advantage of the structure of the residuated lattice.
ABSTRACT We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.
H. Bello, P. Jiménez, C. Bejines. Examining fuzzy number approximation through a topological algebraic approach. Computational and Applied Mathematics 45, 81 (2026).
ABSTRACT In this paper, we delve into the study of fuzzy number approximation by LR fuzzy numbers, shedding light on their algebraic properties. We present a solid approach to approximate fuzzy numbers keeping the same expected interval and core proving that such approximation is additive and continuous under a wide family of distances. As a key part of this construction, we study the set of fuzzy numbers as a topological monoid and develop a process to embed any cancellative abelian topological monoid with open shifts in a topological abelian group. This allows us to demonstrate a highly useful result in the context of this paper: the continuity of homomorphisms between cancellative topological abelian monoids with open shifts is equivalent to its continuity at zero.
D. López-Rodríguez, M. Ojeda-Hernández, A. Mora, C. Bejines. Close-by-One-like algorithms in the fuzzy setting: Theory and experimentation. Fuzzy Sets and Systems 520, Article 109574, 2025.
ABSTRACT In Fuzzy Formal Concept Analysis (FFCA), concept lattices are computed by scaling the problem and applying ordinary FCA algorithms. In this paper, the CbO family of algorithms is extended to work natively in the fuzzy setting, they are proved to be correct and output the whole set of formal concepts, which makes them mathematically equivalent to the scaling approach.
However, experimental results demonstrate the performance improvement of these methods compared to scaling. The paper also discusses a new fuzzy strategy based on blacklisting redundant truth values to enhance the performance of algorithms by taking advantage of the structure of the residuated lattice.
Conference contributions accepted FSTA
28/11/25/10:00 Filed in: Conference papers
O. Krídlo, M. Ojeda-Aciego. Generating Interpretable and User-elicited Fuzzy RDF Properties. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2026.
EXTENDED ABSTRACT
M. Ojeda-Hernández. Direct-optimal systems of attribute implications in fuzzy Formal Concept Analysis. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2026.
EXTENDED ABSTRACT
EXTENDED ABSTRACT
M. Ojeda-Hernández. Direct-optimal systems of attribute implications in fuzzy Formal Concept Analysis. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2026.
EXTENDED ABSTRACT
Participation CONCEPTS'25
13/09/25/11:21 Filed in: Conference participation
Intl Joint Conf on Conceptual Knowledge Structures (Concepts'25). Cluj-Napoca, Romania, September 8-12, 2025
Back from the conference Concepts’25 held in the Babeș-Bolyai University. Our group organized the workshop “Late Breaking Advances on Conceptual Structures” and presented the keywork “Systems of implications obtained using the Carve decomposition of a formal context”.
A very good conference with a lot of interesting presentations and discussions, and even an open problem posed by Prof Bernhard Ganter (let's see what happens with it).
ESTYLF conference organized
06/09/25/13:26 Filed in: Chairing | Organization of conference
XXIII Spanish Fuzzy Logic and Technology conference (ESTYLF) in Rota
The XXIII edition of the Spanish Conference on Fuzzy Logic and Technology (ESTYLF) has been co-chaired by Maru Cornejo (Univ. Cádiz), Manuel Ojeda-Aciego, and Juan Moreno (Univ. Castillas-La Mancha), and organised by Jesús Medina (from Univ. Cádiz).
Our group presented one key-work "On direct systems of implications with graded attributes" by Domingo López, and presented by Manuel Ojeda-Hernández.
Participation EUSFLAT'25
28/07/25/11:52 Filed in: Conference participation
Conference of the European Society of Fuzzy Logic and Technology, EUSFLAT, Riga, Latvia, July 21-25, 2025
As usual a very well-attended conference in which our team presented four contributions: two position papers and two key-work papers. The titles of the talks were "Studying the structure generated by subsets of ƒ-indexes of inclusion" presented by M. Ojeda-Aciego, "Weighted Quantile Approach to Time Series Forecasting Using Fuzzy-Probabilistic Inference Systems" presented by our Czech colleague M. Holčapek, and "On direct systems of implications with graded attributes" and "Kernel operators on trellises" presented by M. Ojeda-Hernández.
We had the opportunity to work with our external collaborators Bernard De Baets and Irina Perfilieva, and also meet other colleagues with which we had interesting discussions on research topics, such as Martin Štěpnička and Lluís Godo. In the picture, our team members together with our colleagues Inma P. Cabrera and Pablo Cordero.
Participation CMMSE'25
12/07/25/11:32 Filed in: Conference participation
Computational and Mathematical Methods in Science and Engineering, CMMSE, Rota, Spain, July 7-12, 2025
Our team presented two contributions in this conference: one position paper and one key-work paper. The titles of the talks were "ƒ-index of inclusion and Armstrong axioms: preliminary results" and "On direct systems of implications with graded attributes".
Journal paper accepted MATHEMATICS
12/06/25/11:03 Filed in: Journal paper
C. Díaz-Montarroso, N. Madrid, E. Ramírez-Poussa. Correctness of Fuzzy Inference Systems Based on f-Inclusion. Mathematics 2025, 13, 1897.
ABSTRACT Recent work has shown that the f -index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to a Fuzzy Description Logic LU enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal.
ABSTRACT Recent work has shown that the f -index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to a Fuzzy Description Logic LU enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal.
Conference papers accepted EUSFLAT
27/05/25/13:02 Filed in: Conference paper
N. Madrid, M. Ojeda-Aciego. Studying the structure generated by subsets of ƒ-indexes of inclusion.14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Key-Work Abstract The ƒ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the ƒ-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 ƒ-index of inclusion.
M. Holcapek, N. Cao, R. Valasek, N. Madrid, T. Tichy, D. Nedela. Weighted Quantile Approach to Time Series Forecasting Using Fuzzy-Probabilistic Inference Systems.14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Contributed Paper Abstract This talk introduces a novel time series forecasting method based on a fuzzy-probabilistic inference system. The central concept is the use of an IF–THEN rule system, where antecedents are represented by fuzzy sets forming a fuzzy partition of the time domain, and consequents are quantile functions that characterize the conditional distribution of time series values over each antecedent.
M. Ojeda-Hernández, D. López Rodríguez. On direct systems of implications with graded attributes. 14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Key-Work Abstract In this paper the problem of defining direct systems of implications in the fuzzy setting is studied. The directness of systems allows a quick computation of the closure operator in cases such as Fuzzy Formal Concept Analysis. Characterizing these properties in algebraic terms is deeply linked to Simplification Logic. After the theoretical results, some thoughts on algorithms to provide direct systems are also considered.
I.P. Cabrera, P. Cordero, B. De Baets, E. Muñoz-Velasco, M. Ojeda-Hernández. Kernel operators on trellises. 14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Contributed Paper Abstract In this work, we focus on interesting mathematical structures that are less known than lattices, namely the class of pseudo-ordered set, and in particular the subclass of trellises. We address the study of kernel operators and their counterparts, closure operators, within the general framework of pseudo-ordered sets and trellises. We also explore Galois connections which are intimately linked to those notions.
Key-Work Abstract The ƒ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the ƒ-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 ƒ-index of inclusion.
M. Holcapek, N. Cao, R. Valasek, N. Madrid, T. Tichy, D. Nedela. Weighted Quantile Approach to Time Series Forecasting Using Fuzzy-Probabilistic Inference Systems.14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Contributed Paper Abstract This talk introduces a novel time series forecasting method based on a fuzzy-probabilistic inference system. The central concept is the use of an IF–THEN rule system, where antecedents are represented by fuzzy sets forming a fuzzy partition of the time domain, and consequents are quantile functions that characterize the conditional distribution of time series values over each antecedent.
M. Ojeda-Hernández, D. López Rodríguez. On direct systems of implications with graded attributes. 14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Key-Work Abstract In this paper the problem of defining direct systems of implications in the fuzzy setting is studied. The directness of systems allows a quick computation of the closure operator in cases such as Fuzzy Formal Concept Analysis. Characterizing these properties in algebraic terms is deeply linked to Simplification Logic. After the theoretical results, some thoughts on algorithms to provide direct systems are also considered.
I.P. Cabrera, P. Cordero, B. De Baets, E. Muñoz-Velasco, M. Ojeda-Hernández. Kernel operators on trellises. 14th Conference of the European Society for Fuzzy Logic and Technology, Riga, 2025.
Contributed Paper Abstract In this work, we focus on interesting mathematical structures that are less known than lattices, namely the class of pseudo-ordered set, and in particular the subclass of trellises. We address the study of kernel operators and their counterparts, closure operators, within the general framework of pseudo-ordered sets and trellises. We also explore Galois connections which are intimately linked to those notions.