G. Cz\'edli's tolerance factor lattice construction, and weak ordered relations

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 $R:=\ \leq \circ T\circ \leq$.