# A Comprehensive Survey of Fuzzy Implication Functions

arXiv: https://arxiv.org/abs/2503.05702 · HTML: https://mlsanity.com/paper/2503.05702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 127 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Built on by (most cited first, 2 of 2)

- [A global view of diverse construction methods of fuzzy implication functions rooted on F-chains](https://mlsanity.com/paper/2509.16298/) (2025)
- [On the Non-Uniqueness of Representation of (U,N)-Implications](https://mlsanity.com/paper/2509.16299/) (2025)

## Abstract (arXiv)

Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval [0,1]. While existing literature often focuses on a limited number of families, in the last ten years many new families have been introduced, each defined by specific construction methods and having different key properties. This survey aims to provide a comprehensive and structured overview of the diverse families of fuzzy implication functions, emphasizing their motivations, properties, and potential applications. By organizing the information schematically, this document serves as a valuable resource for both theoretical researchers seeking to avoid redundancy and practitioners looking to select appropriate operators for specific applications.