May 2022
Journal paper accepted
30/05/22/11:27 Filed in: Journal paper
N. Madrid, C. Cornelis. Kitainik axioms do not characterize the class of inclusion measures based on contrapositive fuzzy implications. Information Sciences, 2022. To appear.
ABSTRACT In this short communication, we refute the conjecture by Fodor and Yager that the class of inclusion measures proposed by Kitainik coincides with that of inclusion measures based on contrapositive fuzzy implications. In particular, we show that the conjecture only holds when the considered universe of discourse is finite.
ABSTRACT In this short communication, we refute the conjecture by Fodor and Yager that the class of inclusion measures proposed by Kitainik coincides with that of inclusion measures based on contrapositive fuzzy implications. In particular, we show that the conjecture only holds when the considered universe of discourse is finite.
Journal papers accepted
30/05/22/10:10 Filed in: Journal papers
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero and E. Muñoz-Velasco. Fuzzy Closure Relations. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The concept of closure operator is key in several branches of mathematics. In this paper, closure operators are extended to relational structures, more specifically to fuzzy relations in the framework of complete fuzzy lattices. The core of the work is the search for a suitable definition of (strong) fuzzy closure relation, that is, a fuzzy relation whose relation with fuzzy closure systems is one-to-one.The study of the properties of fuzzy closure systems and fuzzy relations helps narrow down this exploration until an appropriate definition is settled.
W. Conradie, D. Della Monica, E. Muñoz-Velasco, G. Sciavicco, I.E. Stan. Fuzzy Halpern and Shoham’s Interval Temporal Logics. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal re- lations and propositional labels in a definite, crisp way. In this paper, follow- ing the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.
ABSTRACT The concept of closure operator is key in several branches of mathematics. In this paper, closure operators are extended to relational structures, more specifically to fuzzy relations in the framework of complete fuzzy lattices. The core of the work is the search for a suitable definition of (strong) fuzzy closure relation, that is, a fuzzy relation whose relation with fuzzy closure systems is one-to-one.The study of the properties of fuzzy closure systems and fuzzy relations helps narrow down this exploration until an appropriate definition is settled.
W. Conradie, D. Della Monica, E. Muñoz-Velasco, G. Sciavicco, I.E. Stan. Fuzzy Halpern and Shoham’s Interval Temporal Logics. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal re- lations and propositional labels in a definite, crisp way. In this paper, follow- ing the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.
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.