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A logical study of local and global graded similarities

AuthorsArmengol, Eva ; Dellunde, Eva; García-Cerdaña, Àngel
KeywordsFuzzy relations
Fuzzy class theories
Global similarity
Local similarity
Aggregation operator
Degree of similarity
First order sentences
Fuzzy binary relations
Issue DateApr-2015
PublisherTaylor & Francis
CitationApplied Artificial Intelligence 29: 424- 444 (2015)
AbstractIn 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.
Identifiersdoi: 10.1080/08839514.2015.1026657
issn: 1087-6545
Appears in Collections:(IIIA) Artículos
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