On the characterization of the structure of distributive uninorms

TL;DR

This paper provides a complete characterization of distributive uninorms, revealing that the second uninorm must be locally internal on a specific subset, thereby deepening understanding of their algebraic structure.

Contribution

It introduces a full structural characterization of distributive uninorms, highlighting the local internality condition of the second uninorm on a key subset.

Findings

Second uninorm must be locally internal on A(e)

Complete structural characterization of distributive uninorms

Enhanced understanding of their algebraic properties

Abstract

This paper focuses on distributive uninorms, which induce structures of commutative ordered semirings. We will show that the second uninorm must be locally internal on $A(e)$, and will present a complete characterization of the structure of such uninorms.