Conference papers
Conference papers accepted
01/07/22/10:17
N. Madrid, M. Ojeda-Aciego. Nuevos resultados sobre el f-índice de inclusión. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT En este documento presentamos alguno de los últimos resultados teóricos obtenidos sobre el f-índice de inclusión. Estos resultados motivan el uso de dicho índice como una nueva forma de representar la inclusión entre dos conjuntos difusos y como un operador de inferencia lógica. En este resumen recordamos dos: se satisfacen los axiomas de Sinha-Dougherty (convenientemente adaptados al marco teórico del f-índice de inclusión) y, además, corresponde a una elección optimal de una implicación difusa residuada para llevar a cabo la inferencia Modus Ponens.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, Manuel Ojeda-Aciego. Conexiones de Galois relacionales difusas entre digrafos transitivos difusos. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Presentamos una versión difusa de la noción de conexión de Galois relacional entre grafos dirigidos transitivos difusos (digrafos T-difusos) en el entorno específico en el que el álgebra subyacente de valores de verdad es un álgebra de Heyting completa. Los componentes de dicha conexión de Galois difusa son relaciones difusas que satisfacen ciertas propiedades razonables expresadas en términos de lo que denominamos "full powering". Además, proporcionamos una condición necesaria y suficiente bajo la cual es posible construir un adjunto a la derecha para una relación difusa dada entre un digrafo T-difuso y un conjunto no estructurado.
F. Pérez-Gámez, P. Cordero, M. Enciso, Á. Mora, M. Ojeda-Aciego. Análisis de conceptos formales bajo una visión intuicionista. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Contextos formales parciales son contextos con tres valores que nos permite establecer cuando una propiedad se satisface o no. Además, permite representar situaciones en las que existe ignorancia sobre si una propiedad se satisface o no. Esto puede ser bastante útil en diferentes aspectos como cuando hay información desconocida o, también, cuando aparece la información desconocida debido a intentamos reducir el tamaño de un contexto formal agrupando filas. En este artículo extendemos estas nociones e ideas para añadir grados de conocimiento.
M. Ojeda-Hernandez, I. P. Cabrera, P. Cordero, E. Muñoz-Velasco. Un estudio preliminar de relaciones de clausura difusas. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Los operadores de clausura son elementos clave de las matemáticas tanto puras como aplicadas. Esta contribución trata la búsqueda de una definición de relación de clausura difusa que extienda de manera apropiada el concepto de operador de clausura en el marco de los retículos completos difusos. La condición que se busca extender es la correspondencia biyectiva con los sistemas de clausura difusos. Se parte de las definiciones existentes de relación de clausura difusa y se acotan las condiciones necesarias para la existencia de la biyección hasta que se encuentran las condiciones óptimas.
P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Uso de Lógica Difusa para Construir un Sistema Recomendador Médico. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT En este trabajo, se propone un motor automatizado basado en la Lógica de Simplificación difusa para realizar sugerencias a los usuarios.
Los sistemas de recomendación conversacional han demostrado ser un buen enfoque en telemedicina, construyendo un diálogo entre el usuario y el recomendador basado en las preferencias del usuario proporcionadas en cada paso de la conversación. Aquí proponemos un sistema de recomendación conversacional para el diagnóstico médico utilizando la lógica difusa.
ABSTRACT En este documento presentamos alguno de los últimos resultados teóricos obtenidos sobre el f-índice de inclusión. Estos resultados motivan el uso de dicho índice como una nueva forma de representar la inclusión entre dos conjuntos difusos y como un operador de inferencia lógica. En este resumen recordamos dos: se satisfacen los axiomas de Sinha-Dougherty (convenientemente adaptados al marco teórico del f-índice de inclusión) y, además, corresponde a una elección optimal de una implicación difusa residuada para llevar a cabo la inferencia Modus Ponens.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, Manuel Ojeda-Aciego. Conexiones de Galois relacionales difusas entre digrafos transitivos difusos. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Presentamos una versión difusa de la noción de conexión de Galois relacional entre grafos dirigidos transitivos difusos (digrafos T-difusos) en el entorno específico en el que el álgebra subyacente de valores de verdad es un álgebra de Heyting completa. Los componentes de dicha conexión de Galois difusa son relaciones difusas que satisfacen ciertas propiedades razonables expresadas en términos de lo que denominamos "full powering". Además, proporcionamos una condición necesaria y suficiente bajo la cual es posible construir un adjunto a la derecha para una relación difusa dada entre un digrafo T-difuso y un conjunto no estructurado.
F. Pérez-Gámez, P. Cordero, M. Enciso, Á. Mora, M. Ojeda-Aciego. Análisis de conceptos formales bajo una visión intuicionista. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Contextos formales parciales son contextos con tres valores que nos permite establecer cuando una propiedad se satisface o no. Además, permite representar situaciones en las que existe ignorancia sobre si una propiedad se satisface o no. Esto puede ser bastante útil en diferentes aspectos como cuando hay información desconocida o, también, cuando aparece la información desconocida debido a intentamos reducir el tamaño de un contexto formal agrupando filas. En este artículo extendemos estas nociones e ideas para añadir grados de conocimiento.
M. Ojeda-Hernandez, I. P. Cabrera, P. Cordero, E. Muñoz-Velasco. Un estudio preliminar de relaciones de clausura difusas. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT Los operadores de clausura son elementos clave de las matemáticas tanto puras como aplicadas. Esta contribución trata la búsqueda de una definición de relación de clausura difusa que extienda de manera apropiada el concepto de operador de clausura en el marco de los retículos completos difusos. La condición que se busca extender es la correspondencia biyectiva con los sistemas de clausura difusos. Se parte de las definiciones existentes de relación de clausura difusa y se acotan las condiciones necesarias para la existencia de la biyección hasta que se encuentran las condiciones óptimas.
P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Uso de Lógica Difusa para Construir un Sistema Recomendador Médico. Simp. Nacional sobre Tecnología y Lógica Difusa (ESTYLF), Toledo, 2022.
ABSTRACT En este trabajo, se propone un motor automatizado basado en la Lógica de Simplificación difusa para realizar sugerencias a los usuarios.
Los sistemas de recomendación conversacional han demostrado ser un buen enfoque en telemedicina, construyendo un diálogo entre el usuario y el recomendador basado en las preferencias del usuario proporcionadas en cada paso de la conversación. Aquí proponemos un sistema de recomendación conversacional para el diagnóstico médico utilizando la lógica difusa.
Conference papers accepted
10/05/22/10:29
D. López-Rodríguez, Á. Mora, M. Ojeda-Hernandez. Revisiting Algorithms for Fuzzy Concept Lattices. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT A central notion in Formal Concept Analysis is the concept lattice. This lattice allows describing a hierarchical biclustering between objects and attributes of a formal context, whose hierarchy is defined by an order that expresses the specialisation-generalisation relationship between concepts. It is a fundamental way of representing the knowledge implicit in the context. Therefore, in practice, due to its theoretical complexity, it is necessary to define computationally efficient algorithms for its calculation. In the literature, several algorithms, using different approaches, have been proposed for the computation of the lattice in the classical framework, where the presence of an attribute in an object is modelled as a binary value, indicating that the attribute is either present or absent. However, it is possible to extend this framework to take into account the different degrees to which an attribute could be present in an object. Through this extension, it is possible to model fuzzy situations where the attribute is not 100% present in an object, giving flexibility to the model. In this paper, we review the best-known algorithms for the calculation of the concept lattice in the binary version, and we extend them for the calculation of the fuzzy concept lattice, presenting the most significant differences with respect to the original binary versions. In addition, we will present examples of the execution of these new versions of the algorithms.
M. Ojeda-Hernandez, I. P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure systems over Heyting algebras as fixed points of a fuzzy Galois connection. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT Closure is a key concept in several branches of mathematics. This work presents a definition of fuzzy closure relation and relational closure system on fuzzy transitive digraphs. The core of the paper is the study of the properties of these structures. As expected, fuzzy closure relations and relational closure systems are related, but the relationship among them is not one-to-one. Last section of the paper shows the search for some characterizations for that one-to-one relation to hold.
F. Pérez-Gámez, P. Cordero, M. Enciso, Á. Mora, M. Ojeda-Aciego. Partial formal contexts with degrees. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT Partial formal contexts are trivalued contexts that, besides allowing to establish whether a property is satisfied or not, allow to represent situations in which there is ignorance about whether a property is satisfied. This can be useful, not only for when the modeled phenomenon has intrinsically unknown information, but also when summarizing information from a formal context by grouping similar rows. In this paper we prospect for its extension including degrees of knowledge.
F.J. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. On the affordance-theoretic bases of the landscape of knowledge paradigm. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT In this paper we set out to understand the cognitive basis of Formal Concept Analysis used as an Exploratory Data Analysis framework under the guise of the Landscapes of Knowledge metaphor introduced by Wille. We show that it can be re-interpreted and extended in the framework of the Theory of Affordances from Ecological Psychology to provide not only different affordances for different flavours of formal analysis of the information captured by a formal context, but also a theory that sheds light on how we learn to do it, Perceptual Learning. This raises the issue of what it is that a formal analysis of a formal context provides. We introduce the concept of formal qualia as basic, incomparable, privative items of information afforded by each possible analysis and illustrate these concepts by the formal qualia provided by Formal Concept, Independence and Equivalence Analysis.
ABSTRACT A central notion in Formal Concept Analysis is the concept lattice. This lattice allows describing a hierarchical biclustering between objects and attributes of a formal context, whose hierarchy is defined by an order that expresses the specialisation-generalisation relationship between concepts. It is a fundamental way of representing the knowledge implicit in the context. Therefore, in practice, due to its theoretical complexity, it is necessary to define computationally efficient algorithms for its calculation. In the literature, several algorithms, using different approaches, have been proposed for the computation of the lattice in the classical framework, where the presence of an attribute in an object is modelled as a binary value, indicating that the attribute is either present or absent. However, it is possible to extend this framework to take into account the different degrees to which an attribute could be present in an object. Through this extension, it is possible to model fuzzy situations where the attribute is not 100% present in an object, giving flexibility to the model. In this paper, we review the best-known algorithms for the calculation of the concept lattice in the binary version, and we extend them for the calculation of the fuzzy concept lattice, presenting the most significant differences with respect to the original binary versions. In addition, we will present examples of the execution of these new versions of the algorithms.
M. Ojeda-Hernandez, I. P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure systems over Heyting algebras as fixed points of a fuzzy Galois connection. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT Closure is a key concept in several branches of mathematics. This work presents a definition of fuzzy closure relation and relational closure system on fuzzy transitive digraphs. The core of the paper is the study of the properties of these structures. As expected, fuzzy closure relations and relational closure systems are related, but the relationship among them is not one-to-one. Last section of the paper shows the search for some characterizations for that one-to-one relation to hold.
F. Pérez-Gámez, P. Cordero, M. Enciso, Á. Mora, M. Ojeda-Aciego. Partial formal contexts with degrees. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT Partial formal contexts are trivalued contexts that, besides allowing to establish whether a property is satisfied or not, allow to represent situations in which there is ignorance about whether a property is satisfied. This can be useful, not only for when the modeled phenomenon has intrinsically unknown information, but also when summarizing information from a formal context by grouping similar rows. In this paper we prospect for its extension including degrees of knowledge.
F.J. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. On the affordance-theoretic bases of the landscape of knowledge paradigm. Intl. Conf. on Concept Lattices and their Applications (CLA), Tallinn, 2022.
ABSTRACT In this paper we set out to understand the cognitive basis of Formal Concept Analysis used as an Exploratory Data Analysis framework under the guise of the Landscapes of Knowledge metaphor introduced by Wille. We show that it can be re-interpreted and extended in the framework of the Theory of Affordances from Ecological Psychology to provide not only different affordances for different flavours of formal analysis of the information captured by a formal context, but also a theory that sheds light on how we learn to do it, Perceptual Learning. This raises the issue of what it is that a formal analysis of a formal context provides. We introduce the concept of formal qualia as basic, incomparable, privative items of information afforded by each possible analysis and illustrate these concepts by the formal qualia provided by Formal Concept, Independence and Equivalence Analysis.
Conference papers accepted
18/04/22/12:28
M. Ojeda-Hernandez, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Relational extension of closure structures. Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT Closure is a key concept in several branches of mathematics. This work presents a definition of fuzzy closure relation and relational closure system on fuzzy transitive digraphs. The core of the paper is the study of the properties of these structures. As expected, fuzzy closure relations and relational closure systems are related, but the relationship among them is not one-to-one. Last section of the paper shows the search for some characterizations for that one-to-one relation to hold.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, M. Ojeda-Aciego, B. De Baets. On the definition of fuzzy relational Galois connections between fuzzy transitive digraphs. Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT In this paper, we continue the study of different generalizations on the notion of Galois connection. In previous works, we focused on cases where the (co)domain has the structure of a transitive digraph or a fuzzy transitive digraph. Now, we extend it to the fuzzy relational framework. Specifically, we present a suitable notion of fuzzy relational Galois connection between fuzzy transitive digraphs where both components are now fuzzy relations and the underlying truth value algebra is a complete Heyting algebra. This notion of fuzzy relational Galois connection inherits the most interesting characterisation of the notion of (crisp) relational Galois connection.
F.J. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. On Embedding Finite Lattices into the Lattice of Divisibility. Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT In this paper we provide an embedding of finite lattices into (N,|), the lattice of divisibility of natural numbers. For that purpose, we explore two representations: vector clocks, a device to provide a virtual time used in distributed systems that has gained traction as a finite lattice representation, and the log-prime function that transforms natural numbers into sequences of prime exponents. Using a generalized log-prime function and its inverse we describe how to embed any finite (width, height) lattice into (N, |) and provide examples for such process, prior to analysing the affordances of such encoding vis-a-vis the representation of non-global, distributed time. We also discuss how this representation may help improve the affordances of using complete lattices in data analysis both for time- and non-time related data.
F. Pérez-Gámez, P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Computing the Mixed Concept Lattice. Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT The classical approach on Formal Concept Analysis (FCA) extracts knowledge from a binary table K=(G,M,I) taking into account the existing relationships (given by the binary relation I) between objects G and attributes M. Thus, this classical setting accounts only for positive information. Particularly, FCA allows to define and compute the concept lattice from this positive information. As an extension of this framework, some works consider not only this positive information, but also the negative information that is explicit when objects have no relation to specific attributes. These works, therefore, use the apposition of positive and negative information to compute the mixed concept lattice. In this paper, we propose to establish the relationships between extents and intents of concepts in the positive, negative and the mixed concept lattices and how to address an incremental algorithm to compute the latter by merging the knowledge on the positive and negative ones previously obtained with classical methods.
ABSTRACT Closure is a key concept in several branches of mathematics. This work presents a definition of fuzzy closure relation and relational closure system on fuzzy transitive digraphs. The core of the paper is the study of the properties of these structures. As expected, fuzzy closure relations and relational closure systems are related, but the relationship among them is not one-to-one. Last section of the paper shows the search for some characterizations for that one-to-one relation to hold.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, M. Ojeda-Aciego, B. De Baets. On the definition of fuzzy relational Galois connections between fuzzy transitive digraphs. Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT In this paper, we continue the study of different generalizations on the notion of Galois connection. In previous works, we focused on cases where the (co)domain has the structure of a transitive digraph or a fuzzy transitive digraph. Now, we extend it to the fuzzy relational framework. Specifically, we present a suitable notion of fuzzy relational Galois connection between fuzzy transitive digraphs where both components are now fuzzy relations and the underlying truth value algebra is a complete Heyting algebra. This notion of fuzzy relational Galois connection inherits the most interesting characterisation of the notion of (crisp) relational Galois connection.
F.J. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. On Embedding Finite Lattices into the Lattice of Divisibility. Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT In this paper we provide an embedding of finite lattices into (N,|), the lattice of divisibility of natural numbers. For that purpose, we explore two representations: vector clocks, a device to provide a virtual time used in distributed systems that has gained traction as a finite lattice representation, and the log-prime function that transforms natural numbers into sequences of prime exponents. Using a generalized log-prime function and its inverse we describe how to embed any finite (width, height) lattice into (N, |) and provide examples for such process, prior to analysing the affordances of such encoding vis-a-vis the representation of non-global, distributed time. We also discuss how this representation may help improve the affordances of using complete lattices in data analysis both for time- and non-time related data.
F. Pérez-Gámez, P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Computing the Mixed Concept Lattice. Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Milan, 2022.
ABSTRACT The classical approach on Formal Concept Analysis (FCA) extracts knowledge from a binary table K=(G,M,I) taking into account the existing relationships (given by the binary relation I) between objects G and attributes M. Thus, this classical setting accounts only for positive information. Particularly, FCA allows to define and compute the concept lattice from this positive information. As an extension of this framework, some works consider not only this positive information, but also the negative information that is explicit when objects have no relation to specific attributes. These works, therefore, use the apposition of positive and negative information to compute the mixed concept lattice. In this paper, we propose to establish the relationships between extents and intents of concepts in the positive, negative and the mixed concept lattices and how to address an incremental algorithm to compute the latter by merging the knowledge on the positive and negative ones previously obtained with classical methods.
Conference papers accepted
02/11/21/10:10
O. Krídlo, M. Ojeda-Aciego. Lower Sugeno-like Integral for Multi-Adjoint FCA. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The proposed relationship between L-fuzzy measures, integrals and isotone concept-forming operators on a Girard monoid has recently been used to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We further continue generalizing the construction aiming at the framework of multi-adjoint formal concept analysis. At this level of generality it is still possible to define a multi-adjoint analogy for lower Sugeno integral at the price of slight modifications in the definition of the underlying adjoint triple. The notion of upper Sugeno integral requires a much more complete treatment including negations, implications with many properties, etc. and is an interesting piece of future work.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure relations. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The concept of closure operator is extended to a fuzzy relation in a complete fuzzy lattice, and the existence of a one-to-one relation between fuzzy closure systems and fuzzy closure relations is studied. First, a suitable definition of fuzzy closure relation must be established, using the existing definitions in the literature as a start point. Next, once the definition is set, one must find two functions such that fuzzy closure systems map to fuzzy closure relations and vice versa. Finally, this correspondence is proved to be one-to-one.
ABSTRACT The proposed relationship between L-fuzzy measures, integrals and isotone concept-forming operators on a Girard monoid has recently been used to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We further continue generalizing the construction aiming at the framework of multi-adjoint formal concept analysis. At this level of generality it is still possible to define a multi-adjoint analogy for lower Sugeno integral at the price of slight modifications in the definition of the underlying adjoint triple. The notion of upper Sugeno integral requires a much more complete treatment including negations, implications with many properties, etc. and is an interesting piece of future work.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure relations. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The concept of closure operator is extended to a fuzzy relation in a complete fuzzy lattice, and the existence of a one-to-one relation between fuzzy closure systems and fuzzy closure relations is studied. First, a suitable definition of fuzzy closure relation must be established, using the existing definitions in the literature as a start point. Next, once the definition is set, one must find two functions such that fuzzy closure systems map to fuzzy closure relations and vice versa. Finally, this correspondence is proved to be one-to-one.
Conference papers accepted
12/07/21/11:10
O. Krídlo, M. Ojeda-Aciego. Sugeno integral for Atanassov intuitionistic fuzzy sets. Eur. Symp. on Computational Intelligence and Mathematics, Budapest, 2021.
ABSTRACT We work on the recently proposed relationship between L-fuzzy measures and integrals and isotone concept-forming operators on a Girard monoid in order to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We also provide some examples on the practical interpretation of the new proposed notion.
M. Ojeda-Aciego, J.M. Rodriguez-Jimenez. Advances in forgery detection of driving licences using truthfulness degrees. Eur. Symp. on Computational Intelligence and Mathematics, Budapest, 2021.
ABSTRACT We develop a methodology which allows to detect forgeries in driving licences based on an analysis of two serial codes usually present in licences issued in European countries. Results from the initial analysis of licences issued in France and Italy are presented.
ABSTRACT We work on the recently proposed relationship between L-fuzzy measures and integrals and isotone concept-forming operators on a Girard monoid in order to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We also provide some examples on the practical interpretation of the new proposed notion.
M. Ojeda-Aciego, J.M. Rodriguez-Jimenez. Advances in forgery detection of driving licences using truthfulness degrees. Eur. Symp. on Computational Intelligence and Mathematics, Budapest, 2021.
ABSTRACT We develop a methodology which allows to detect forgeries in driving licences based on an analysis of two serial codes usually present in licences issued in European countries. Results from the initial analysis of licences issued in France and Italy are presented.
Conference papers accepted
24/06/21/10:10
D. López-Rodríguez, P. Cordero, M. Enciso, Á. Mora. How to provide light to COVID data by means of FCA. RealDataFCA workshop (jointly with ICFCA'21), 2021.
ABSTRACT COVID data are usually presented in a non-structured format and mainly focused on healthy issues (incidence, mortality, etc). At the same time, Governments have designed a set of measures to deal with the Pandemic. In addition, several institutions have studied the economical effects of the situation in each country. In this work, we combine these three data sources and illustrate how Formal Concept Analysis can become a useful tool to discover relationships among these three views of the situation: health, politics and economy. Our aim is to provide an implication-driven approach to discover knowledge behind the data.
P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Topic Modelling in Social Networks with Formal Concept Analysis. Computational Mathematical Methods in Science and Engineering, Rota, 2021.
ABSTRACT In the age of social networks, the amount of the written material published every day exceeds our processing capacity. Topic models can help to organise and to understand extensive collections of unstructured text documents. In machine learning and natural language processing, a topic model is a statistical model for discovering the abstract ``topics'' in a collection of documents, uncovering hidden semantic structures and clusters of similar words.
To approach topic modelling in social networks, we use Formal Concept Analysis, a mathematical tool firmly based on lattice theory and logic. Our approach uses the knowledge contained in the concept lattice to extract the topics. Thus, this approach to topic modelling is not statistical. For example, we do not need to assume a prior distribution of terms. Instead, the actual data structure is used to infer the semantic relationships between attributes.
An experiment with a dataset with tweets about some hashtags is conducted with our approach to show how Formal Concept Analysis can be used in Social Network Analysis. In addition, a comparison with classical techniques is being addressed.
N. Madrid, M. Ojeda-Aciego. Residuated structures via the f-index of inclusion. Computational and Mathematical Methods in Science and Engineering, Rota, 2021.
ABSTRACT The origin of the $f$-index of inclusion can be dated back to the incorporation of negation connectives in multi-adjoint logic programs and, hence, to study inconsistency and, its sibling, coherence. As a result, it was clear that (in-)consistency should not be considered as a crisp notion when applied in (general) fuzzy logic theories, and different approaches were proposed for this goal. We introduced the notion weak-contradiction as a generalization of the notion of coherence in the general framework of fuzzy set theory. Soon after introducing measures for weak-contradiction, we started to imagine some kind of function-based approach to measuring the inclusion between fuzzy sets, and presented the first ideas about the $f$-index of inclusion. We have recently recovered the idea of relating the two research lines emerged in parallel, namely the weak-contradiction and the $f$-index of inclusion, with satisfactory results.
In this work we show that the $f$-index of inclusion is very related to fuzzy implications and, in fact, three different residuated structures can be obtained.
ABSTRACT COVID data are usually presented in a non-structured format and mainly focused on healthy issues (incidence, mortality, etc). At the same time, Governments have designed a set of measures to deal with the Pandemic. In addition, several institutions have studied the economical effects of the situation in each country. In this work, we combine these three data sources and illustrate how Formal Concept Analysis can become a useful tool to discover relationships among these three views of the situation: health, politics and economy. Our aim is to provide an implication-driven approach to discover knowledge behind the data.
P. Cordero, M. Enciso, D. López-Rodríguez, Á. Mora. Topic Modelling in Social Networks with Formal Concept Analysis. Computational Mathematical Methods in Science and Engineering, Rota, 2021.
ABSTRACT In the age of social networks, the amount of the written material published every day exceeds our processing capacity. Topic models can help to organise and to understand extensive collections of unstructured text documents. In machine learning and natural language processing, a topic model is a statistical model for discovering the abstract ``topics'' in a collection of documents, uncovering hidden semantic structures and clusters of similar words.
To approach topic modelling in social networks, we use Formal Concept Analysis, a mathematical tool firmly based on lattice theory and logic. Our approach uses the knowledge contained in the concept lattice to extract the topics. Thus, this approach to topic modelling is not statistical. For example, we do not need to assume a prior distribution of terms. Instead, the actual data structure is used to infer the semantic relationships between attributes.
An experiment with a dataset with tweets about some hashtags is conducted with our approach to show how Formal Concept Analysis can be used in Social Network Analysis. In addition, a comparison with classical techniques is being addressed.
N. Madrid, M. Ojeda-Aciego. Residuated structures via the f-index of inclusion. Computational and Mathematical Methods in Science and Engineering, Rota, 2021.
ABSTRACT The origin of the $f$-index of inclusion can be dated back to the incorporation of negation connectives in multi-adjoint logic programs and, hence, to study inconsistency and, its sibling, coherence. As a result, it was clear that (in-)consistency should not be considered as a crisp notion when applied in (general) fuzzy logic theories, and different approaches were proposed for this goal. We introduced the notion weak-contradiction as a generalization of the notion of coherence in the general framework of fuzzy set theory. Soon after introducing measures for weak-contradiction, we started to imagine some kind of function-based approach to measuring the inclusion between fuzzy sets, and presented the first ideas about the $f$-index of inclusion. We have recently recovered the idea of relating the two research lines emerged in parallel, namely the weak-contradiction and the $f$-index of inclusion, with satisfactory results.
In this work we show that the $f$-index of inclusion is very related to fuzzy implications and, in fact, three different residuated structures can be obtained.
Conference papers accepted
12/05/20/10:16
Inma P. Cabrera, P. Cordero, E. Muñoz and M. Ojeda-Aciego. Galois connections between unbalanced structures in a fuzzy framework. 18th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Lisboa, 2020.
ABSTRACT The construction of Galois connections between unbalanced structures has received considerable attention in the recent years.
In a nutshell, the problem is to find a right adjoint of a mapping defined between sets with unbalanced structure; in this paper we survey recent results obtained in this framework, focusing specially on the fuzzy structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.
F. Valverde, C. Peláez, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Exploratory Data Analysis of Multi-label Classification Tasks with Formal Context Analysis. Concept Lattices and their Applications (CLA), Tallinn, 2020.
ABSTRACT We introduce a new framework, Formal Context Analysis (FxA), for the exploratory analysis of data tasks cast in the guise of formal contexts. FxA gathers a number of results from Formal Concpt Analysis, Formal Independence Analysis and Formal Equivalence Analysis to enhance the establishment and processing of hypothesis about data. We apply this framework to the study of the Multi-label Classification (MLC) task and obtain a number of results of technical nature about how the induction mechanism for MLC classifiers should proceed. The application is based on an analysis of multilabel classification from the standpoint of FxA.
N. Madrid and M. Ojeda-Aciego. Inconsistency in fuzzy logic systems. International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2020.
ABSTRACT Different notions of consistency which are equivalent in the classical case are no longer equivalent in a fuzzy framework; this leads to different potential notions of consistency in a fuzzy setting. The underlying problem is to consider "consistency" as a crisp property; instead, we propose to consider a gradual notion of consistency, and different measures of consistency are introduced and analyzed.
N. Madrid. Towards the use of quantile fuzzy transforms for the construction of fuzzy association rules. IEEE Int Conf on Fuzzy Systems (FUZZ-IEEE), Glasgow, 2020.
ABSTRACT This paper analyzes the possibility of defining fuzzy association rules by means of direct quantiles F-transforms. The set of fuzzy association rules is used in a fuzzy inference system, defined by means of the inverse quantile F-transform. The obtained inference system reminds the Takagi-Sugeno one due to the use of a weighted sum to perform the inference. However, there is an important difference: the output is a fuzzy set and, as a result, we require the use of a defuzzification procedure. In addition, in this paper we prove experimentally that the fuzzy set obtained as the output of the proposed inference system is related to a probability distribution.
N. Madrid and E. Ramírez-Poussa. Representative Set of Objects in Rough Sets Based on Galois Connections. International Joint Conference on Rough Sets (IJCRS), La Habana, 2020.
ABSTRACT This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on rough sets. The idea behind such a notion is to consider subsets of objects that characterize the different classes given by a decision system. Besides the formal definition of representative set of objects of a decision class, we present different mathematical properties of such sets and a relationship with classification tasks based on rough sets.
ABSTRACT The construction of Galois connections between unbalanced structures has received considerable attention in the recent years.
In a nutshell, the problem is to find a right adjoint of a mapping defined between sets with unbalanced structure; in this paper we survey recent results obtained in this framework, focusing specially on the fuzzy structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.
F. Valverde, C. Peláez, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Exploratory Data Analysis of Multi-label Classification Tasks with Formal Context Analysis. Concept Lattices and their Applications (CLA), Tallinn, 2020.
ABSTRACT We introduce a new framework, Formal Context Analysis (FxA), for the exploratory analysis of data tasks cast in the guise of formal contexts. FxA gathers a number of results from Formal Concpt Analysis, Formal Independence Analysis and Formal Equivalence Analysis to enhance the establishment and processing of hypothesis about data. We apply this framework to the study of the Multi-label Classification (MLC) task and obtain a number of results of technical nature about how the induction mechanism for MLC classifiers should proceed. The application is based on an analysis of multilabel classification from the standpoint of FxA.
N. Madrid and M. Ojeda-Aciego. Inconsistency in fuzzy logic systems. International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2020.
ABSTRACT Different notions of consistency which are equivalent in the classical case are no longer equivalent in a fuzzy framework; this leads to different potential notions of consistency in a fuzzy setting. The underlying problem is to consider "consistency" as a crisp property; instead, we propose to consider a gradual notion of consistency, and different measures of consistency are introduced and analyzed.
N. Madrid. Towards the use of quantile fuzzy transforms for the construction of fuzzy association rules. IEEE Int Conf on Fuzzy Systems (FUZZ-IEEE), Glasgow, 2020.
ABSTRACT This paper analyzes the possibility of defining fuzzy association rules by means of direct quantiles F-transforms. The set of fuzzy association rules is used in a fuzzy inference system, defined by means of the inverse quantile F-transform. The obtained inference system reminds the Takagi-Sugeno one due to the use of a weighted sum to perform the inference. However, there is an important difference: the output is a fuzzy set and, as a result, we require the use of a defuzzification procedure. In addition, in this paper we prove experimentally that the fuzzy set obtained as the output of the proposed inference system is related to a probability distribution.
N. Madrid and E. Ramírez-Poussa. Representative Set of Objects in Rough Sets Based on Galois Connections. International Joint Conference on Rough Sets (IJCRS), La Habana, 2020.
ABSTRACT This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on rough sets. The idea behind such a notion is to consider subsets of objects that characterize the different classes given by a decision system. Besides the formal definition of representative set of objects of a decision class, we present different mathematical properties of such sets and a relationship with classification tasks based on rough sets.
Conference papers accepted
15/01/20/08:51
N. Madrid and M. Ojeda-Aciego. New measures of inclusion between fuzzy sets in terms of the f-index of inclusion. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT The notion of inclusion is one of the most basic relations between sets, however, there is not a consensus about how to extend such a notion in fuzzy set theory. We introduce an alternative approach to previous methods in the literature in which we make use of the so-called f-index of inclusion. This approach has a main difference with respect to previous ones: instead of a value in [0,1], the measure of inclusion is identified with a function.
In this paper, using the f-index of inclusion we define two measures of inclusion in the standard sense, i.e., taking a value in [0,1] and then, we show that both measures are in accordance with the standard axiomatic approaches about measures of inclusion in the literature.
W. Conradie, D. Della Monica, E, Muñoz-Velasco and G. Sciavicco. An Approach to Fuzzy Modal Logic of Time Intervals. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT Temporal reasoning based on intervals is nowadays ubiquitous in artificial intelligence, and the most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the eighties. There has been a great effort in the past in studying the expressive power and computational properties of the satisfiability problem for HS and its fragments, but only recently HS has been proposed as a suitable formalism for artificial intelligence applications. Such applications highlighted some of the intrinsic limits of HS: sometimes, when dealing with real-life data, many times one is not able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, among others, we present a fuzzy generalization of HS that partially solves such problems of expressive power, and we prove that, as in the crisp case, its satisfiability problem is generally undecidable.
ABSTRACT The notion of inclusion is one of the most basic relations between sets, however, there is not a consensus about how to extend such a notion in fuzzy set theory. We introduce an alternative approach to previous methods in the literature in which we make use of the so-called f-index of inclusion. This approach has a main difference with respect to previous ones: instead of a value in [0,1], the measure of inclusion is identified with a function.
In this paper, using the f-index of inclusion we define two measures of inclusion in the standard sense, i.e., taking a value in [0,1] and then, we show that both measures are in accordance with the standard axiomatic approaches about measures of inclusion in the literature.
W. Conradie, D. Della Monica, E, Muñoz-Velasco and G. Sciavicco. An Approach to Fuzzy Modal Logic of Time Intervals. 24th Eur Conf on Artificial Intelligence (ECAI), Santiago de Compostela, 2020.
ABSTRACT Temporal reasoning based on intervals is nowadays ubiquitous in artificial intelligence, and the most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the eighties. There has been a great effort in the past in studying the expressive power and computational properties of the satisfiability problem for HS and its fragments, but only recently HS has been proposed as a suitable formalism for artificial intelligence applications. Such applications highlighted some of the intrinsic limits of HS: sometimes, when dealing with real-life data, many times one is not able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, among others, we present a fuzzy generalization of HS that partially solves such problems of expressive power, and we prove that, as in the crisp case, its satisfiability problem is generally undecidable.
Conference paper accepted
02/09/19/11:38
P. Cordero, I. Fortes, I.P. de Guzmán and S. Sánchez. Simplifying Inductive Schemes in Temporal Logic. 26th Int Symp on Temporal Representation and Reasoning (TIME), Málaga, 2019.
ABSTRACT In propositional temporal logic, the combination of the connectives “tomorrow” and “always in the future” requires the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula.
ABSTRACT In propositional temporal logic, the combination of the connectives “tomorrow” and “always in the future” requires the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula.
Conference papers accepted
09/07/19/09:10
European Symposium on Computational Intelligence and Mathematics (ESCIM), Toledo, 2019.
- N. Madrid and M. Ojeda-Aciego. Some relationships between the notions of f-inclusion and f-contradiction.
ABSTRACT In this paper we analyse the relationships between the notions of f-inclusion and f-weak-contradiction. In particular, we present some theoretical results that relate both notions by means of negation operators (used to define complements of fuzzy sets) and Galois connections - O. Krídlo, M. Ojeda-Aciego, T. Put, and M. Reformat. On some categories underlying knowledge graphs.
ABSTRACT This paper proposes a method to provide a categorical structure for RDF-based data representing descriptions of entities. This is the first step towards our aim to further develop the underlying categorical structure so that we can eventually provide an internal logic which enables us to focus on analysis of properties of entities. - P. Cordero, M. Enciso, A. Mora, M. Ojeda-Aciego, and C. Rossi. Interactive search by means of the minimal generators.
ABSTRACT If-then rules are frequently used as basic elements for knowledge representation in several areas. In Formal Concept Analysis, these rules are the so-called implications and can be used to find minimal generators in a symbolic way by using logic. The computation of all minimal generators is exponential. Here, we provide a novel lazy algorithm with polynomial delay in which minimal generators are used as forks in a map to guide an interactive search..
Conference papers accepted
15/05/19/09:03
J.M. Rodriguez-Jimenez and M. Ojeda-Aciego. Analysing patterns in false documents with Formal Concept Analysis to detect forgers. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT Europe's system of open frontiers, commonly known as "Schengen", let people from different countries travel without problems crossing these frontiers. Different documents from these countries, not only European, could be found in road checkpoints, and Police forces have the problem that do not have an international database to know whether they are false or not. Some immigrants with legal problems in their original countries who need a new identity, or want a driver license to access to specific jobs, contact forgers who provide false documents with different levels of authenticity. Countries and Police Forces should improve their methodologies, by ensuring that staff is increasingly better able to detect false of falsified documents through their examination, and follow patterns to detect and ubícate these forgers. In this paper, we propose a method based on Formal Concept Analysis with negative attributes that allows Police forces analysing false documents, and provides a guide to enforce the detection of forgers.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Aciego. Relational Galois connections between fuzzy t-digraphs. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT The notion of relational Galois connection is extended to be applied between fuzzy transitive directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering.
N. Madrid and M. Ojeda-Aciego. Towards a measure of inclusion from the index of inclusion between fuzzy sets. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT Despite of the notion of inclusion between fuzzy sets has taken a great interest of a large number of researchers since Zadeh presented his seminal work in 1965, there is not a consensus about how to extend such a notion in fuzzy set theory yet. In this contribution we recall a recent fresh approach that represent the inclusion between two fuzzy sets by mean of a mapping (called index of inclusion) instead of a degree, as the standard approaches do. Moreover, we present a measure of inclusion (i.e. a degree) defined from our index of inclusion that allows to compare our approach directly with others in the literature.
D. López, A. Mora. Recommendations in CDSS using Fuzzy Formal Concept Analysis. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT One of the hot topics in clinical research is hidden knowledge discovery in datasets with a high number of features (variables or attributes). We approach how to provide recommendations in Clinical Decision Support Systems (CDSS) to guide the experts in the diagnostic process. We work by mining graded implications from the dataset using the NEXTCLOSURE algorithm for Graded Attributes. Reasoning with these graded implications is done with the so-called Fuzzy Attribute Simplification Logic. As the number of graded implications mined from the fuzzy formal context is huge and with a high degree of redundancy, the objective is to obtain a equivalent set without redundancy, by applying the rules of the logic..
ABSTRACT Europe's system of open frontiers, commonly known as "Schengen", let people from different countries travel without problems crossing these frontiers. Different documents from these countries, not only European, could be found in road checkpoints, and Police forces have the problem that do not have an international database to know whether they are false or not. Some immigrants with legal problems in their original countries who need a new identity, or want a driver license to access to specific jobs, contact forgers who provide false documents with different levels of authenticity. Countries and Police Forces should improve their methodologies, by ensuring that staff is increasingly better able to detect false of falsified documents through their examination, and follow patterns to detect and ubícate these forgers. In this paper, we propose a method based on Formal Concept Analysis with negative attributes that allows Police forces analysing false documents, and provides a guide to enforce the detection of forgers.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Aciego. Relational Galois connections between fuzzy t-digraphs. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT The notion of relational Galois connection is extended to be applied between fuzzy transitive directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering.
N. Madrid and M. Ojeda-Aciego. Towards a measure of inclusion from the index of inclusion between fuzzy sets. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT Despite of the notion of inclusion between fuzzy sets has taken a great interest of a large number of researchers since Zadeh presented his seminal work in 1965, there is not a consensus about how to extend such a notion in fuzzy set theory yet. In this contribution we recall a recent fresh approach that represent the inclusion between two fuzzy sets by mean of a mapping (called index of inclusion) instead of a degree, as the standard approaches do. Moreover, we present a measure of inclusion (i.e. a degree) defined from our index of inclusion that allows to compare our approach directly with others in the literature.
D. López, A. Mora. Recommendations in CDSS using Fuzzy Formal Concept Analysis. Intl Conference Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2019.
ABSTRACT One of the hot topics in clinical research is hidden knowledge discovery in datasets with a high number of features (variables or attributes). We approach how to provide recommendations in Clinical Decision Support Systems (CDSS) to guide the experts in the diagnostic process. We work by mining graded implications from the dataset using the NEXTCLOSURE algorithm for Graded Attributes. Reasoning with these graded implications is done with the so-called Fuzzy Attribute Simplification Logic. As the number of graded implications mined from the fuzzy formal context is huge and with a high degree of redundancy, the objective is to obtain a equivalent set without redundancy, by applying the rules of the logic..
Conference papers accepted
13/04/19/08:57
F.J. Valverde-Albacete, C. Peláez-Moreno, P. Cordero and M. Ojeda-Aciego. Formal Equivalence Analysis. Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Prague, 2019
ABSTRACT Following R. Wille's lead and suggestion we set out to design a new kind of view onto a formal context analogous but different to Formal Concept Analysis (FCA) and Formal Independent Analysis (FIA). In this instance, we choose to analyse the information in the incidence table in terms of the partitions induced on the sets of objects and attributes by the some functions of single attributes and objects of the context. These functions constitute a left adjunction between sets of objects and attributes and we later lift this left adjunction to partitions of the objects and attributes. Therefore we refer to this new view onto the formal context as Formal Equivalence Analysis (FEA). Rather than looking on the effect of these partitions on set representation, as in Rough Sets, we try to make explicit the information in the context.
Inma P. Cabrera, P. Cordero, E. Muñoz and M. Ojeda-Aciego. Towards fuzzy relational Galois connections between fuzzy t-digraphs. Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Prague, 2019
ABSTRACT In this paper, we give the first steps towards a formal definition of fuzzy relational Galois connection between fuzzy sets with arbitrary fuzzy transitive relations (fuzzy T-digraphs), where the two components of the connection are fuzzy relations. To this end we consider, on the one hand, our definition of relational Galois connection between T-digraphs in the crisp case; and, on the other hand, our definition of fuzzy relational Galois connection between fuzzy preorders. We compare both definitions and conclude that some (fuzzy) generalization of the notion of clique is needed.
ABSTRACT Following R. Wille's lead and suggestion we set out to design a new kind of view onto a formal context analogous but different to Formal Concept Analysis (FCA) and Formal Independent Analysis (FIA). In this instance, we choose to analyse the information in the incidence table in terms of the partitions induced on the sets of objects and attributes by the some functions of single attributes and objects of the context. These functions constitute a left adjunction between sets of objects and attributes and we later lift this left adjunction to partitions of the objects and attributes. Therefore we refer to this new view onto the formal context as Formal Equivalence Analysis (FEA). Rather than looking on the effect of these partitions on set representation, as in Rough Sets, we try to make explicit the information in the context.
Inma P. Cabrera, P. Cordero, E. Muñoz and M. Ojeda-Aciego. Towards fuzzy relational Galois connections between fuzzy t-digraphs. Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Prague, 2019
ABSTRACT In this paper, we give the first steps towards a formal definition of fuzzy relational Galois connection between fuzzy sets with arbitrary fuzzy transitive relations (fuzzy T-digraphs), where the two components of the connection are fuzzy relations. To this end we consider, on the one hand, our definition of relational Galois connection between T-digraphs in the crisp case; and, on the other hand, our definition of fuzzy relational Galois connection between fuzzy preorders. We compare both definitions and conclude that some (fuzzy) generalization of the notion of clique is needed.
Conference paper accepted
11/03/19/08:51
Inma P. Cabrera, P. Cordero, E. Muñoz and M. Ojeda-Aciego. A relational extension of Galois Connections. Intl Conf on Formal Concept Analysis (ICFCA), Frankfurt, 2019.
ABSTRACT In this paper, we focus on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations as well. Specifically, we introduce the notion of relational Galois connection between two transitive digraphs, study some of its properties and its relationship with other existing approaches in the literature.
ABSTRACT In this paper, we focus on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations as well. Specifically, we introduce the notion of relational Galois connection between two transitive digraphs, study some of its properties and its relationship with other existing approaches in the literature.