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A logical study of local and global graded similarities
Armengol, Eva (Institut d'Investigació en Intel·ligència Artificial)
Dellunde i Clavé, Pilar (Universitat Autònoma de Barcelona. Departament de Filosofia)
García-Cerdaña, Àngel (Universitat Pompeu Fabra. Departament de Tecnologies de la Informació i les Comunicacions)

Fecha: 2015
Resumen: In this work we study the relationship between global and local similarities in the graded framework of fuzzy class theory (FCT), in which there already exists a graded notion of similarity. In FCT we can express the fact that a fuzzy relation is reflexive, symmetric, or transitive up to a certain degree, and similarity is defined as a first-order sentence, which is the fusion of three sentences corresponding to the graded notions of reflexivity, symmetry, and transitivity. This allows us to speak in a natural way of the degree of similarity of a relation. We consider global similarities defined from local similarities using t-norms as aggregation operators, and we obtain some results in the framework of FCT that, adequately interpreted, allow us to say that when we take a t-norm as an aggregation operator, the properties of reflexivity, symmetry, and transitivity of fuzzy binary relations are inherited from the local to the global level, and that the global similarity is a congruence if some of the local similarities are congruences.
Derechos: Tots els drets reservats.
Lengua: Anglès.
Documento: article ; recerca ; acceptedVersion
Publicado en: Applied artificial intelligence, Vol. 29, núm. 5 (2015) , p. 424-444, ISSN 0883-9514

DOI: 10.1080/08839514.2015.1026657

16 p, 198.6 KB

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