A comparative study of ideals in fuzzy orders

TL;DR

This paper compares three types of ideals in fuzzy order theory—forward Cauchy, flat, and irreducible ideals—and explores their roles in linking fuzzy order with fuzzy topology.

Contribution

It provides a comparative analysis of different ideals in fuzzy order theory and examines their connections to fuzzy topology, offering new insights into their relationships.

Findings

Identifies key differences among the three types of ideals.

Establishes connections between fuzzy order ideals and fuzzy topology.

Highlights the roles of these ideals in fuzzy order theory.

Abstract

This paper presents a comparative study of three kinds of ideals in fuzzy order theory: forward Cauchy ideals (generated by forward Cauchy nets), flat ideals and irreducible ideals, including their role in connecting fuzzy order with fuzzy topology.