concept lattice

Let and be sets whose elements we call objects and attributes respectively. Let . We say that object has attribute iff . The triple is called a context. For any set of objects, define

In other words, is the set of all attributes that are common to all objects in . Similarly, for any set of attributes, set

In other words, is the set of all objects having all the attributes in . We call a pair a concept of the context provided that

If is a concept, then is called the extent of the concept and the intent of the concept.

Given a context . Let be the set of all concepts of . Define a binary relation^{👁 Mathworld
👁 Planetmath}
on by iff . Then makes a lattice^{👁 Mathworld
👁 Planetmath}
, and in fact a complete lattice^{👁 Mathworld
👁 Planetmath}
. together with is called the concept latice of the context .