# Characterizations of idempotent discrete uninorms

## TL;DR

This paper characterizes idempotent discrete uninorms using axioms, bisymmetry, and graphical methods, offering new insights into their structure and properties.

## Contribution

It provides the first axiomatic and graphical characterizations of idempotent discrete uninorms, expanding understanding of their mathematical structure.

## Key findings

- Axiomatic characterization using three conditions
- Alternative characterization via bisymmetry
- Graphical contour plot representations

## Abstract

In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open questions for further research.