On Factorization of Concept Lattices by Incompatible Tolerances*

摘要

It is a well-known fact that complete tolerance relations on concept lattices are in one-to-one correspondence with some superrelations (called block relations) of the incidence relation of the underlying formal context. However, sometimes it is useful to consider more general superrelations of the incidence relation, leading to tolerance relations, not compatible with the lattice structure of the concept lattice. In this paper, we give a characterization of such tolerances and present a mathematical framework for factorizing any complete lattice by such incompatible tolerances.