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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 $.

G. Czédli’s tolerance factor lattice construction and weak ordered relations