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.
RSME 2024
06/02/24/10:54 Filed in: Conference participation | Chairing
Congreso Bienal de la Real Sociedad Matemática Española. Pamplona, 22 - 26 enero 2024
Manuel Ojeda-Hernández was co-organizer of the special session "Mathematical Developments in Artificial Intelligence and Machine Learning", which turned out to be the one which attracted most papers out of the 25 different special sessions.
He also presented a paper entitled "Algoritmos CbO para el cálculo del retículo de conceptos".
Conference papers accepted: ESCIM
06/02/24/10:27 Filed in: Conference papers
I. Perfilieva, N. Madrid, M. Ojeda-Aciego, P. Artiemjew, A. Niemczynowicz. Extreme Learning Machine as a New Learning Paradigm: Pros and Cons. Eur. Symp. on Computational Intelligence and Mathematics, ESCIM, 2024.
ABSTRACT We analyze the validity of the Extreme Learning Machine principles proposed as a new learning methodology for Single Layer Feedforward Neural Networks. We show that despite the empirical success of ELM, its theoretical platform does not have a rigorous mathematical justification. To do this, we show that two main statements in its seminal paper do not have correct proofs and are in fact incorrect. Moreover, we create a dataset that provides a counterexample to the theoretical assertions done about the ELM learning algorithm.
F. Pérez-Gámez, C. Bejines, P. Cordero, D. López-Rodríguez, M. Ojeda-Hernández. Inheritance of completeness between systems of strong and weak implications. Eur. Symp. on Computational Intelligence and Mathematics, ESCIM, 2024.
ABSTRACT The study of unknown information in formal contexts can be done from two extremely different points of view: working just with the information available at the moment, or exploring all the different values that the unknown information can take.
From these two perspectives, we obtain two kinds of attribute implications: the weak ones which are the attribute implications that hold with the current amount of information, and the strong ones which will also hold under any update of the context. We study whether, given a complete system of weak implications concerning partial formal context, one can extract a complete system of strong ones concerning the same partial formal context.
FSTA 2024
05/02/24/13:20 Filed in: Conference participation
Fuzzy Sets Theory and Applications, Liptovský Ján, Slovak Republic, Jan 28-Feb 2 2024
We presented two works "An FCA-based approach to RDF graphs" (presented by Manuel Ojeda-Aciego) and "Close-by-One strategy for computing the fuzzy concept lattice" (presented by Manuel Ojeda-Hernández).
A nice workshop, plenty of scientific and cultural activities, in which we found some time to work on forthcoming research topics with our collaborator Irina Perfilieva.
Conference papers accepted: FSTA
30/11/23/13:48 Filed in: Conference papers
O. Krídlo, D. López-Rodríguez, M. Ojeda-Aciego, M. Reformat. An FCA-based approach to RDF graphs. Fuzzy Sets Theory and Applications, FSTA, 2024.
ABSTRACT We investigate building a connection between RDF and FCA. The proposed approach transforms an RDF graph, where vertices represent objects of different types and edges represent relationships between these objects, into a series of bipartite graphs. It is achieved by separating edges representing specific relationships, resulting in a clear representation of the relationship of interest without clutter. To address this issue, we propose a bond-based construction of rigorous and benevolent compositions of bipartite graphs. These bipartite graphs are extracted from RDF graphs and combined—using the proposed construction—with external information related to the graphs' entities.
D. López-Rodríguez, M. Ojeda-Hernández, Á. Mora. Close-by-One strategy for computing the fuzzy concept lattice. Fuzzy Sets Theory and Applications, FSTA, 2024.
ABSTRACT We present the extension of CbO-like algorithms to a native fuzzy environment, without scaling, and combining the advantages of the different algorithms to obtain faster results with less computational load. The soundness of these algorithms is presented together with a comparison with existing strategies to show the improvement in both time, number of intents computed and number of tests performed.
Journal paper accepted: Fuzzy Sets and Systems
02/11/23/10:36 Filed in: Journal paper
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.
PhD thesis
24/10/23/10:01 Filed in: PhD thesis
M. Ojeda-Hernández. Fuzzy closure structures and quasi-closed elements on fuzzy complete lattices. PhD thesis, 2023.
A very good dissertation (Summa Cum Laude) by Manuel on an important topic of our work package on Foundations.
