Formal Concepts and Maximal Compatibility Blocks

Abstract

An alternative perspective of formal concept is presented. Given the finite formal context, the incidence relation is seen as the universe of discourse since it is a subset of the Cartesian product from objects set to attributes set, and then the compatibility relation on the universe is induced. It is proved that formal concepts are precisely maximal compatibility blocks with respect to the induced compatibility relation. Some properties of formal concept are also discussed in terms of maximal compatibility blocks.