# Crisp complexity of fuzzy classifiers

arXiv: https://arxiv.org/abs/2504.15791 · HTML: https://mlsanity.com/paper/2504.15791/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Metrics for Multi-Class Classification: an Overview](https://mlsanity.com/paper/2008.05756/) (2020)
- [ARTxAI: Explainable Artificial Intelligence Curates Deep Representation Learning for Artistic Images using Fuzzy Techniques](https://mlsanity.com/paper/2308.15284/) (2023)
- [Backpropagation-Free Learning Method for Correlated Fuzzy Neural Networks](https://mlsanity.com/paper/2012.01935/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Fast Interpretable Fuzzy Tree Learner](https://mlsanity.com/paper/2512.11616/) (2025)

## Abstract (arXiv)

Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger traction outside of fuzzy venues, because users sometimes do not know about fuzzy and because fuzzy partitions are not so easy to interpret in some situations. In this work, we propose a methodology to reduce fuzzy rule-based classifiers to crisp rule-based classifiers. We study different possible crisp descriptions and implement an algorithm to obtain them. Also, we analyze the complexity of the resulting crisp classifiers. We believe that our results can help both fuzzy and non-fuzzy practitioners understand better the way in which fuzzy rule bases partition the feature space and how easily one system can be translated to another and vice versa. Our complexity metric can also help to choose between different fuzzy classifiers based on what the equivalent crisp partitions look like.