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

TL;DR

This paper explores the relationship between weak ordered relations and factor lattices derived from tolerances, showing that the Dedekind-Mac Neille completion of a quotient lattice is isomorphic to a concept lattice constructed from a specific context.

Contribution

It establishes a novel isomorphism between the Dedekind-Mac Neille completion of a tolerance quotient lattice and a concept lattice from a related context, linking tolerances to weak ordered relations.

Findings

Dedekind-Mac Neille completion of L/T is isomorphic to a concept lattice.

Connection between weak ordered relations and tolerance-based factor lattices.

Provides a new perspective on lattice completions and tolerance relations.

Abstract

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 $.