FUZZ-IEEE 2024, Yokohama, Japan
15/07/24/10:22 Filed in: Conference participation
Int Conf on Fuzzy Systems, FUZZ-IEEE, Yokohama, Japan, Jun 30-Jul 5, 2024
FUZZ-IEEE has been a part of the WCCI (World Congress on Computational Intelligence) jointly with the International Joint Conference on Neural Networks IJCNN and the Congress on Evolutionary Computation CEC. In this edition our group has presented the work "Enhancing performance of FCA algorithms via rearrangement of formal contexts" (by Domingo López-Rodríguez and Manuel Ojeda-Hernández, who presented the paper).
In the picture below, we can see Manuel together with members of the group M-CIS from Universidad de Cádiz.
CMMSE 2024
09/07/24/11:34 Filed in: Conference participation
Int Conf on Computational and Mathematical Methods in Science and Engineering, CMMSE, Rota, Cádiz, Spain, July 2-8, 2024
As in previous years, we included in CMMSE a special session entitled Mathematical Methods in Computer Science, in cooperation with the Royal Spanish Society of Mathematics. The session was well-attended. We presented the work "New results on f-indexes of inclusion: composition as a fuzzy conjunction".
ESTYLF conference organized
We have co-chaired the Spanish Fuzzy Logic and Technology conference (ESTYLF) in Coruña
The most recent edition of the Spanish Conference on Fuzzy Logic and Technology (ESTYLF) has been co-chaired by Manuel Ojeda-Aciego and Jesús Medina (from Univ. Cádiz).
Our group presented three communications:
- F. Pérez-Gámez and C. Bejines. Álgebras de Heyting débiles: una generalización para retículos no distributivos.
- I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Estructuras de clausura difusas como puntos fijos de conexiones de Galois.
- N. Madrid and M. Ojeda-Aciego. El f-índice de inclusión como par adjunto óptimo para modus ponens difuso.
We also participated as co-editors of the proceedings of CAEPIA'24, published by Springer.
Journal papers accepted
27/06/24/13:14 Filed in: Journal papers
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.
ESCIM 2024
28/05/24/13:25 Filed in: Conference participation
European Symposium on Computational Intelligence and Mathematics, ESCIM, Kraków, Poland, May 12-15, 2024
A well-attended conference in which our work presented three works written jointly with other researchers, some of them already in our team and some external ones. The titles of the talks were "Extreme Learning Machine as a New Learning Paradigm: Pros and Cons", "Inheritance of completeness between systems of strong and weak implications" and "Legal and technical challenges of AI in the field of Criminal investigations".
We had the opportunity to meet again a number of colleagues, László Koczy, Juan Moreno, and Jesús Medina among others, in order to discuss prospects of future work or continue the existing ones. In the picture, our team members together with Irina Perfilieva (external member).
Conference papers accepted
18/05/24/12:28 Filed in: Conference papers
N. Madrid, M. Ojeda-Aciego. New results on f-indexes of inclusion: composition as a fuzzy conjunction. Intl Conf on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2024.
ABSTRACT We show that composition behaves like a fuzzy conjunction on the set of indexes of inclusion. By restricting the latter set to a join-subsemilattice of indexes we can find a representation theorem for monoids on the unit interval in terms of the composition and subsets of indexes. Furthermore, we show that composition (as a fuzzy conjunction) admits two residuated implications, hence forming an adjoint triple.
D. López-Rodríguez, M. Ojeda-Hernández. Rearrangement of fuzzy formal contexts for reducing cost of algorithms. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts.
O. Krídlo, D. López-Rodríguez, L. Antoni, P. Eliaš, S. Krajči, and M. Ojeda-Aciego. Connecting concept lattices with bonds between L-fuzzy formal contexts by external information. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT We have delved into the interpretation of two novel methods for selecting appropriate bonds between L-fuzzy formal contexts, based on the use of the rigorous and benevolent concept-forming operators. The strategy presented therein for the construction of the rigorous and the benevolent bonds is knowledge-driven: the presence of external information about the strength of the connection about the attribute sets, given by an operator p: A_1 x A_2 -> L, induces both types of bond. Therefore, these new methods overcome the difficulty of bond interpretation by taking advantage of the incorporation of knowledge into the problem. In that paper, we formally verified that the bonds built using this strategy produce results coherent with the piece of external information used.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Fuzzy relational Galois connections between fuzzy transitive digraphs. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this work, we present an adequate notion of fuzzy relational Galois connection with both components now being fuzzy relations between two universes each endowed with binary transitive fuzzy relations. We focus on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra.
C. Díaz-Montarroso, N. Madrid, E. Ramírez-Poussa. Towards a generalized modus ponens based on the f-index of inclusion. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT This paper proposes a generalized modus ponens and a generalized modus tollens based on the f-index of inclusion. Moreover, we analyze the properties of generalized modus ponens and generalized modus tollens according to the axioms proposed by Baldwin and Pilsworth.
ABSTRACT We show that composition behaves like a fuzzy conjunction on the set of indexes of inclusion. By restricting the latter set to a join-subsemilattice of indexes we can find a representation theorem for monoids on the unit interval in terms of the composition and subsets of indexes. Furthermore, we show that composition (as a fuzzy conjunction) admits two residuated implications, hence forming an adjoint triple.
D. López-Rodríguez, M. Ojeda-Hernández. Rearrangement of fuzzy formal contexts for reducing cost of algorithms. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts.
O. Krídlo, D. López-Rodríguez, L. Antoni, P. Eliaš, S. Krajči, and M. Ojeda-Aciego. Connecting concept lattices with bonds between L-fuzzy formal contexts by external information. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT We have delved into the interpretation of two novel methods for selecting appropriate bonds between L-fuzzy formal contexts, based on the use of the rigorous and benevolent concept-forming operators. The strategy presented therein for the construction of the rigorous and the benevolent bonds is knowledge-driven: the presence of external information about the strength of the connection about the attribute sets, given by an operator p: A_1 x A_2 -> L, induces both types of bond. Therefore, these new methods overcome the difficulty of bond interpretation by taking advantage of the incorporation of knowledge into the problem. In that paper, we formally verified that the bonds built using this strategy produce results coherent with the piece of external information used.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Fuzzy relational Galois connections between fuzzy transitive digraphs. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this work, we present an adequate notion of fuzzy relational Galois connection with both components now being fuzzy relations between two universes each endowed with binary transitive fuzzy relations. We focus on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra.
C. Díaz-Montarroso, N. Madrid, E. Ramírez-Poussa. Towards a generalized modus ponens based on the f-index of inclusion. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT This paper proposes a generalized modus ponens and a generalized modus tollens based on the f-index of inclusion. Moreover, we analyze the properties of generalized modus ponens and generalized modus tollens according to the axioms proposed by Baldwin and Pilsworth.
Conference papers accepted ESTYLF
17/04/24/10:15 Filed in: Conference papers
Francisco Pérez-Gámez and Carlos Bejines. Álgebras de Heyting débiles: una generalización para retículos no distributivos. Congreso Español de Tecnología y Lógica Difusa (ESTYLF), Coruña, 2024.
ABSTRACT En este artículo se presentan las álgebras de Heyting débiles. Estas álgebras constituyen una extensión del álgebra de Heyting adaptada a retículos no distributivos. Fijado un retículo, se enumeran condiciones que garantizan la existencia de estas álgebras. Además, se caracterizan en función de los operadores de implicación y se acota su rango.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Estructuras de clausura difusas como puntos fijos de conexiones de Galois. Congreso Español de Tecnología y Lógica Difusa (ESTYLF), Coruña, 2024.
ABSTRACT Las conexiones de Galois parecen estar omnipresentes en las matemáticas. Se han utilizado para modelizar soluciones de problemas tanto puros como orientados a aplicaciones. A lo largo del artículo, el marco general es un retículo completo difuso sobre un retículo residuado completo. En este trabajo, se estudia la existencia de conexiones difusas de Galois (antítonas e isótonas) entre cuatro conjuntos ordenados específicos. Lo más interesante es que los sistemas de cierre difusos, los operadores de cierre difusos y las relaciones de cierre difusas fuertes son conceptos formales (puntos fijos) de estas conexiones de Galois difusas..
N. Madrid and M. Ojeda-Aciego. El f-índice de inclusión como par adjunto óptimo para modus ponens difuso. Congreso Español de Tecnología y Lógica Difusa (ESTYLF), Coruña, 2024.
ABSTRACT Continuamos estudiando las propiedades del f-índice de inclusión y mostramos que, dado un par fijo de conjuntos difusos, su f-índice de inclusión puede vincularse a una conjunción difusa que forma parte de un par adjunto. También mostramos que, cuando este par se utiliza como estructura subyacente para proporcionar una interpretación difusa de la regla de inferencia modus ponens, proporciona el máximo valor de verdad posible en la conclusión entre todos los valores obtenidos por modus ponens difuso utilizando cualquier otro par adjunto posible.
ABSTRACT En este artículo se presentan las álgebras de Heyting débiles. Estas álgebras constituyen una extensión del álgebra de Heyting adaptada a retículos no distributivos. Fijado un retículo, se enumeran condiciones que garantizan la existencia de estas álgebras. Además, se caracterizan en función de los operadores de implicación y se acota su rango.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Estructuras de clausura difusas como puntos fijos de conexiones de Galois. Congreso Español de Tecnología y Lógica Difusa (ESTYLF), Coruña, 2024.
ABSTRACT Las conexiones de Galois parecen estar omnipresentes en las matemáticas. Se han utilizado para modelizar soluciones de problemas tanto puros como orientados a aplicaciones. A lo largo del artículo, el marco general es un retículo completo difuso sobre un retículo residuado completo. En este trabajo, se estudia la existencia de conexiones difusas de Galois (antítonas e isótonas) entre cuatro conjuntos ordenados específicos. Lo más interesante es que los sistemas de cierre difusos, los operadores de cierre difusos y las relaciones de cierre difusas fuertes son conceptos formales (puntos fijos) de estas conexiones de Galois difusas..
N. Madrid and M. Ojeda-Aciego. El f-índice de inclusión como par adjunto óptimo para modus ponens difuso. Congreso Español de Tecnología y Lógica Difusa (ESTYLF), Coruña, 2024.
ABSTRACT Continuamos estudiando las propiedades del f-índice de inclusión y mostramos que, dado un par fijo de conjuntos difusos, su f-índice de inclusión puede vincularse a una conjunción difusa que forma parte de un par adjunto. También mostramos que, cuando este par se utiliza como estructura subyacente para proporcionar una interpretación difusa de la regla de inferencia modus ponens, proporciona el máximo valor de verdad posible en la conclusión entre todos los valores obtenidos por modus ponens difuso utilizando cualquier otro par adjunto posible.
Conference paper accepted FUZZ-IEEE
17/03/24/10:18 Filed in: Conference paper
D. López-Rodríguez and M. Ojeda-Hernández. Enhancing performance of FCA algorithms via rearrangement of formal contexts. Intl Conf on Fuzzy Systems (FUZZ-IEEE), Yokohama, Japan, 2024.
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts..
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts..
Journal paper accepted: Mathematics
13/02/24/10:27 Filed in: Journal paper
C. Bejines, M. Ojeda-Hernández, D. López-Rodríguez. Analysis of fuzzy vector spaces as an algebraic framework for flag codes. Mathematics. 2024
ABSTRACT Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified to the same flag, which naturally induces an equivalence relation on the set of fuzzy vector subspaces. The main contributions of this work are the methodological abstraction of flags and flag codes in terms of fuzzy vector subspaces, as well as the generalisation of three distinct equivalence relations that originated from the fuzzy subgroup theory and study of their connection with flag codes, computing the number of equivalence classes in the discrete case, which represent the number of essentially distinct flags, and a comprehensive analysis of such relations and the properties of the corresponding quotient sets.