Operations and Properties on Lattices and Trellises

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.