April 2019
Conference papers accepted
13/04/19/08:57 Filed in: Conference papers
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.