Multi-scaled concept lattices

This paper proposes a method to reduce the number of concepts still conserving their formal structure. Our main idea is first to gather objects into classes such that the members of the same class share some set of properties, and then define a kind of Galois connection via a concept of inclusion degree in order to cope, to a certain degree (denoted as alpha), with this partition. Thus, a complete lattice called multi-scaled concept lattice or alpha concept lattice can be produced. It is proved that the a concept lattice produced by the original context is equal to the concept lattice produced by the induced alpha context. As a result, we can construct multi-scaled concept lattices from the induced context by using the well-known software of Galicia.