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