  The main results of the paper points out the connection between the weak
ordered relations and factor lattices defined by tolerances. It is proved that
for any tolerance $T$ of a lattice $L$ the Dedekind-Mac Neille completion of
$L/T$ is isomorphic to the concept lattice $\mathcal{L}(L,L,R)$ of the context
$(L,L,R)$, where $R:=\ \leq \circ T\circ \leq $.
