Informatica

The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions.