April 2022
Conference papers accepted
18/04/22/12:28 Filed in: Conference papers
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.