Conference papers
Conference papers accepted: CMMSE, CONCEPTS
18/05/24/12:28
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
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 papers accepted: ESCIM
06/02/24/10:27
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.
D. Pérez-Medina, N. Madrid, P.A. Kowalski. Legal and technical challenges of AI in the field of Criminal investigations. Eur. Symp. on Computational Intelligence and Mathematics, ESCIM, 2024.
ABSTRACT This article addresses critical challenges in the intersection of artificial intelligence, crime investigation and digital forensics, particularly in light of the
proposed Regulation on Artificial Intelligence in the European Union. The focus is on mitigating biases caused by databases and algorithms, with real-world examples
highlighting discriminatory biases in criminal proceedings. The article emphasises the necessity of addressing biases in both data and algorithmic decision-making to
ensure fair outcomes. Another key concern explored is the lack of traceability in AI-based decisions, posing challenges to accountability and transparency, especially,
in the context of criminal investigations. Additionally, the article delves into the protection of private and family data in the vast datasets analysed by AI systems, referencing a legal case that underscores the potential violation of the right to a fair trial. To address this, the article proposes the development of anonymisation
systems to safeguard individuals’ privacy rights. The overarching theme is the need for ethical considerations and legal frameworks to guide the responsible development and deployment of AI tools in digital forensics.
Conference papers accepted: FSTA
30/11/23/13:48
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.
Conference papers accepted: EUSFLAT
01/09/23/12:17
T. Flaminio, Ll. Godo, N. Madrid, M. Ojeda-Aciego. A Logic to Reason About f-Indices of Inclusion over Ł𝑛. Proc. of EUSFLAT 2023.
ABSTRACT In this paper we provide a sound and complete logic to formalise and reason about f-indices of inclusion. The logic is based on finite-valued Lukasiewicz logic and its S5-like modal extension S5(L) with additional unary operators.
Published in Lecture Notes in Computer Science, vol 14069: 530-539, 2023.
M. Ojeda-Hernández, P. Cordero, I.P. Cabrera, E. Muñoz-Velasco. Closure structures as fixed points of some Galois connections. Proc. of EUSFLAT 2023.
Extended abstract published in Book of Abstracts EUSFLAT 2023.
Conference papers accepted: ICCS
01/09/23/12:17
C. Bejines, D. López-Rodríguez, M. Ojeda-Hernández. Aggregation Functions and Extent Structure Preservation in Formal Concept Analysis. Proc. of Int. Conf. on Conceptual Structures.
ABSTRACT Formal Concept Analysis (FCA) is a mathematical framework for analysing data tables that capture the relationship between objects and attributes. The concept lattice derived from such a table is a representation of the implicit knowledge about this relationship, where each concept corresponds to a bicluster of objects and attributes. FCA has been widely used for knowledge acquisition and representation, conceptual data analysis, information retrieval and other applications. In this paper, we use an extension of the classical FCA to deal with fuzzy formal contexts, where the relationship between objects and attributes is modelled by truth values indicating the degree to which an object possesses a property or attribute. Fuzzy Formal Concept Analysis (FFCA) allows us to capture vague or imprecise information and handle uncertainty or ambiguity in data analysis. Our purpose is to use aggregation functions in order to manipulate and explore fuzzy formal concepts in different ways depending on the desired properties or criteria. In this work, we will focus on the structure of the extents of the concept lattice. We define the aggregation of fuzzy extents point-wise and study how it affects its structure. We characterise the aggregation functions that preserve the fuzzy extent structure and show that they depend on the number of objects in the context. Our results contribute to a better understanding of how aggregation functions can be used to manipulate and explore fuzzy formal concepts..
Published as Lecture Notes in Computer Science, vol 14133: 28-35, 2023
M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, E. Muñoz-Velasco. On Pseudointents in Fuzzy Formal Concept Analysis. Proc. of Int. Conf. on Conceptual Structures.
ABSTRACT Formal Concept Analysis (FCA) is a mathematical framework for analysing data tables that capture the relationship between objects and attributes. FCA deals with two main structures of knowledge, namely the concept lattice and the basis of attribute implications. There are several sets of implications in the literature, for instance minimal bases, direct bases or direct minimal bases. In this work we are interested in the concept of pseudointent in the fuzzy framework in order to define the Duquenne-Guigues basis in the fuzzy setting.
Published as Lecture Notes in Computer Science, vol 14133: 36-40, 2023