# On learning capacities of Sugeno integrals with systems of fuzzy relational equations

arXiv: https://arxiv.org/abs/2408.07768 · HTML: https://mlsanity.com/paper/2408.07768/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 1 of 1)

- [Machine Learning with the Sugeno Integral: The Case of Binary Classification](https://mlsanity.com/paper/2007.03046/) (2020)

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

- [Approximate matrices of systems of max-min fuzzy relational equations](https://mlsanity.com/paper/2504.16042/) (2025)
- [A Sugeno Integral View of Binarized Neural Network Inference](https://mlsanity.com/paper/2604.17967/) (2026)

## Abstract (arXiv)

In this article, we introduce a method for learning a capacity underlying a Sugeno integral according to training data based on systems of fuzzy relational equations. To the training data, we associate two systems of equations: a max-min system and a min-max system. By solving these two systems (in the case that they are consistent) using Sanchez's results, we show that we can directly obtain the extremal capacities representing the training data. By reducing the max-min (resp. min-max) system of equations to subsets of criteria of cardinality less than or equal to q (resp. of cardinality greater than or equal to n-q), where n is the number of criteria, we give a sufficient condition for deducing, from its potential greatest solution (resp. its potential lowest solution), a q-maxitive (resp. q-minitive) capacity. Finally, if these two reduced systems of equations are inconsistent, we show how to obtain the greatest approximate q-maxitive capacity and the lowest approximate q-minitive capacity, using recent results to handle the inconsistency of systems of fuzzy relational equations.