Operations and Properties on Lattices and Trellises
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Date
2025-06-14
Journal Title
Journal ISSN
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Publisher
Mohamed Boudiaf University of M'sila
Abstract
In this thesis, we present various classes of algebraic operations on ordered structures, with a
particular emphasis on bounded lattices and trellises. To this end, we first recall the essential
concepts and properties of binary relations, partially ordered sets, and lattices. We then
extend the classical framework by introducing pseudo-ordered sets and trellises, which
generalize the notion of partial orders by relaxing the transitivity condition. Finally, we focus
on associative binary operations defined on bounded lattices and trellises, and we propose
novel methods for constructing t-norms on trellises.
Description
Keywords
Lattice, Trellis, Binary Operation, T-norm, T-conorm