# Fuzzy Implicative Rules: A Unified Approach

arXiv: https://arxiv.org/abs/2504.03000 · HTML: https://mlsanity.com/paper/2504.03000/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 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)

Rule mining algorithms are one of the fundamental techniques in data mining for disclosing significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rule to provide a solid theoretical framework for any fuzzy rule mining algorithm interested in capturing patterns in terms of logical conditionals rather than the co-occurrence of antecedent and consequent. In particular, we study which properties should satisfy the fuzzy operators to ensure a coherent behavior of different quality measures. As a consequence of this study, we introduce a new property of fuzzy implication functions related to a monotone behavior of the generalized modus ponens for which we provide different valid solutions. Also, we prove that our modeling generalizes others if an adequate choice of the fuzzy implication function is made, so it can be seen as an unifying framework. Further, we provide an open-source implementation in Python for mining fuzzy implicative associative rules. We test the applicability and relevance of our framework for different real datasets and fuzzy operators.