Conference papers accepted
10/05/22/10:29 Filed in: Conference papers
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.