February 2020
Journal paper accepted
26/02/20/08:36 Filed in: Journal paper
E. Ramírez-Poussa, N. Madrid, J. Medina. Rough Sets based on Galois connections. Applied Mathematics and Computer Science 30(2):299-313, 2020.
ABSTRACT Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of the approximation operators are based on an indiscernibility relation, which is an equivalence relation. Later, different papers have motivated the possibility of considering arbitrary relations nevertheless, when arbitrary relations are considered, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution of the arisen problems by presenting an alternative definition of the approximation operators based on the closure and the interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.
ABSTRACT Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of the approximation operators are based on an indiscernibility relation, which is an equivalence relation. Later, different papers have motivated the possibility of considering arbitrary relations nevertheless, when arbitrary relations are considered, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution of the arisen problems by presenting an alternative definition of the approximation operators based on the closure and the interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.
Journal paper accepted
10/02/20/08:47 Filed in: Journal paper
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco, M. Ojeda-Aciego, B. De Baets. Relational Galois connections between transitive fuzzy digraphs. Mathematical Methods in the Applied Sciences 43(9):5673-5680, 2020.
ABSTRACT Fuzzy directed graphs are often chosen as the datatype to model and implement solutions of several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy 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.
ABSTRACT Fuzzy directed graphs are often chosen as the datatype to model and implement solutions of several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy 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.
FSTA 2020
04/02/20/13:54 Filed in: Conference participation
Fuzzy Set Theory and Applications, FSTA 2020
An intense week in Liptovský Ján, Slovakia, full of interaction with other researchers who work in different topics all within the fuzzy umbrella, where we presented the work "Isotone L-fuzzy FCA and categories L-ChuCors and L-Rel".
The next steps on our research line on Galois connections were discussed with Bernard De Baets, and further work on fuzzy mathematical morphology and the F-transform was discussed with Irina Perfilieva, who will be visiting us in some months.