  The skyline concept has been introduced in order to exhibit the best objects
according to all the criterion combinations and makes it possible to analyse
the relationships between skyline objects. Like the data cube, the skycube is
so voluminous that reduction approaches are really necessary. In this paper, we
define an approach which partially materializes the skycube. The underlying
idea is to discard from the representation the skycuboids which can be computed
again the most easily. To meet this reduction objective, we characterize a
formal framework: the agree concept lattice. From this structure, we derive the
skyline concept lattice which is one of its constrained instances. The strong
points of our approach are: (i) it is attribute oriented; (ii) it provides a
boundary for the number of lattice nodes; (iii) it facilitates the navigation
within the Skycuboids.
