Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier

Authors:
Ali Jaoua;Samir Elloumi
Affiliations:
Department of Computer Sciences, Faculty of Sciences, University of Qatar, P.O. Box 2713, Doha, Qatar;Department of Computer Sciences, Faculty of Sciences of Tunis, Campus Universitaire, 1060 Tunis, Tunisia
Venue:
Journal of Systems and Software - Special issue on artificial and computational intelligence for decisions, control, and automation in engineering and industrial applications
Year:
2002

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Abstract

In this paper, we introduce the notion of a real set as an extension of a crisp and a fuzzy set by using sequences of intervals as membership degrees, instead of a single value in [0,1]. We also propose, to extend the notion of Galois connection in a real binary relation as well as the notions of rectangular relation, formal concept and Galois lattice. We present finally a real classifier based on this mathematical foundation.