21 / 12 / 2022 - 18:20 – 18:50

Radeleczki Sándor Lajos

University of Miskolc – Hungary

Tolerance Factor-Lattice Construction and Weak Ordered Relations

Abstract

G. Czédli proved that the blocks of any compatible tolerance T of a lattice L can be ordered in such a way that they form a lattice L/T called the factor lattice of L modulo T. Here we show that the Dedekind–MacNeille completion of the lattice L/T is isomorphic to the concept lattice of the context (L,L,R), where R stands for the reflexive weak ordered relation ≤∘T. Weak ordered relations constitute the generalization of the ordered relations introduced by S. Valentini. Reflexive weak ordered relations can be characterized as compatible reflexive relations on L satisfying R= ≤∘ R∘ ≤.