Pseudo triangular norms on bounded trellises

TL;DR

This paper introduces pseudo-triangular norms on bounded trellises, exploring their properties, constructions, and relationships with isomorphisms, extending the concept of t-norms beyond traditional associative structures.

Contribution

It generalizes t-norms to weakly associative operations on bounded trellises and investigates their properties and relationships with isomorphisms.

Findings

Pseudo-t-norms are weakly associative operations on trellises.

The paper presents constructions of pseudo-t-norms on bounded trellises.

It explores the relationship between pseudo-t-norms and isomorphisms in non-associative contexts.

Abstract

In this paper, we introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and we investigate their various properties and present some constructions of pseudo-t-norms on bounded trellises. Also, we study the T-distributivity on bounded trellises. Moreover, we show the relationship among pseudo-t-norms and isomorphisms on bounded trellises, which are more complicated in absence of the property of (transitivity) associativity of the trellis meet and join operations.