Nullnorms on bounded trellises

TL;DR

This paper introduces nullnorms on bounded trellises, explores their properties, and proposes construction methods based on existing t-norms and t-conorms, supported by illustrative examples.

Contribution

It is the first to define nullnorms on bounded trellises and develop methods for constructing them from existing t-norms and t-conorms.

Findings

Nullnorms can be constructed from t-norms and t-conorms on bounded trellises.

Basic properties of nullnorms on bounded trellises are established.

Illustrative examples demonstrate the application of the proposed methods.

Abstract

In this paper, we introduce the notion of nullnorms on bounded trellises and study some basic properties. Based on the existence of $t$-norms and $t$-conorms on arbitrary bounded trellises, we propose some construction methods of nullnorms on bounded trellises. Moreover, some illustrative examples are provided.