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A binary operation-based representation of a lattice

Mourad Yettou;  Abdelaziz Amroune;  Lemnaouar Zedam — 2019

Kybernetika

In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new...

Compositions of ternary relations

Norelhouda Bakri;  Lemnaouar Zedam;  Bernard De Baets — 2021

Kybernetika

In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.

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