Journal papers
Journal papers accepted FSS, COAM
28/11/25/10:00
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.
Journal papers accepted: IJAR, FSI
27/06/24/13:14
F.J. Talavera, C. Bejines, S. Ardanza-Trevijano, J. Elorza. Aggregation of fuzzy graphs. Intl J of Approximate Reasoning 109243, 2024
ABSTRACT Our study is centered on the aggregation of fuzzy graphs, looking for conditions under which the aggregation process yields another fuzzy graph. We conduct an in-depth analysis of the preservation of several important properties and structures inherent to fuzzy graphs, like paths, cycles, or bridges. In addition we obtain appropriate criteria for when the aggregation of complete fuzzy graphs is again a complete fuzzy graph.
M. Ojeda-Hernández, D. López-Rodríguez, Á. Mora. A Formal Concept Analysis Approach to Hierarchical Description of Malware Threats. Forensic Science International, 2024. To appear.
ABSTRACT The problem of intelligent malware detection has become increasingly relevant in the industry, as there has been an explosion in the diversity of threats and attacks that affect not only small users, but also large organisations and governments. One of the problems in this field is the lack of homogenisation or standardisation in the nomenclature used by different antivirus programs for different malware threats. The lack of a clear definition of what a {category} is and how it relates to individual threats makes it difficult to share data and extract common information from multiple antivirus programs. Therefore, efforts to create a common naming convention and hierarchy for malware are important to improve collaboration and information sharing in this field.
Our approach uses as a tool the methods of Formal Concept Analysis (FCA) to model and attempt to solve this problem. FCA is an algebraic framework able to discover useful knowledge in the form of a concept lattice and implications relating to the detection and diagnosis of suspicious files and threats. The knowledge extracted using this mathematical tool illustrates how formal methods can help prevent new threats and attacks. We will show the results of applying the proposed methodology to the identification of hierarchical relationships between malware.
ABSTRACT Our study is centered on the aggregation of fuzzy graphs, looking for conditions under which the aggregation process yields another fuzzy graph. We conduct an in-depth analysis of the preservation of several important properties and structures inherent to fuzzy graphs, like paths, cycles, or bridges. In addition we obtain appropriate criteria for when the aggregation of complete fuzzy graphs is again a complete fuzzy graph.
M. Ojeda-Hernández, D. López-Rodríguez, Á. Mora. A Formal Concept Analysis Approach to Hierarchical Description of Malware Threats. Forensic Science International, 2024. To appear.
ABSTRACT The problem of intelligent malware detection has become increasingly relevant in the industry, as there has been an explosion in the diversity of threats and attacks that affect not only small users, but also large organisations and governments. One of the problems in this field is the lack of homogenisation or standardisation in the nomenclature used by different antivirus programs for different malware threats. The lack of a clear definition of what a {category} is and how it relates to individual threats makes it difficult to share data and extract common information from multiple antivirus programs. Therefore, efforts to create a common naming convention and hierarchy for malware are important to improve collaboration and information sharing in this field.
Our approach uses as a tool the methods of Formal Concept Analysis (FCA) to model and attempt to solve this problem. FCA is an algebraic framework able to discover useful knowledge in the form of a concept lattice and implications relating to the detection and diagnosis of suspicious files and threats. The knowledge extracted using this mathematical tool illustrates how formal methods can help prevent new threats and attacks. We will show the results of applying the proposed methodology to the identification of hierarchical relationships between malware.
Journal paper accepted: INS, KYB
01/09/23/12:17
O. Krídlo, D. López-Rodríguez, L. Antoni, P. Eliaš, S. Krajči, and M. Ojeda-Aciego. Connecting concept lattices with bonds induced by external information. Information Sciences, 648:Article 119498, 2023.
ABSTRACT In Formal Concept Analysis (FCA), L-bonds represent relationships between L-formal contexts. Choosing the appropriate bond between L-fuzzy formal contexts is an important challenge for its application in recommendation tasks. Recent work introduced two constructions of bonds, given by direct products of two L-fuzzy formal contexts, and showed their usefulness in a particular application. In this paper, we present further theoretical and experimental results on these constructions; in particular, we provide extended interpretations of both rigorous and benevolent concept-forming operators, introduce new theoretical properties of the proposed bonds to connect two concept lattices given external information, and finally present the experimental study of the upper bounds.
C. Bejines. Aggregation of fuzzy vector spaces. Kybernetika 59(5):752-767, 2023.
ABSTRACT This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process. The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome. The second part of the paper centers around the aggregation of similar fuzzy vector subspaces, specifically those belonging to the same equivalence class. This section scrutinizes the challenges and considerations involved in aggregating fuzzy vector subspaces with shared characteristics. The third part of the paper takes a broad perspective, providing an analysis of the aggregation problem of fuzzy vector subspaces from a general standpoint. It examines the fundamental issues, principles, and implications associated with aggregating fuzzy vector subspaces in a comprehensive manner. By elucidating these three key aspects, this paper contributes to the advancement of knowledge in the field of aggregation of algebraic structures, shedding light on the specific domain of fuzzy vector spaces.