Alpha Galois lattices

In many applications there is a need to represent a large number of data by clustering them in a hierarchy of classes. Our basic representation is a Galois lattice, a structure that exhaustively represents the whole set of concepts that are distinguishable given the instance set and the representation language. What we propose here is a method to reduce the size of the lattice, and thus simplify our view of the data, while conserving its formal structure and exhaustivity. For that purpose we use a preliminary partition of the instance set, representing the association of a "type" to each instance. By redefining the notion of extent of a term in order to cope, to a certain degree (denoted as α), with this partition, we define a particular family of Galois lattices denoted as alpha Galois lattices. We also discuss the related implication rules defined as inclusion of such α-extents.