# Maximal Consistent Subsystems of Max-T Fuzzy Relational Equations

arXiv: https://arxiv.org/abs/2311.03059 · HTML: https://mlsanity.com/paper/2311.03059/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 2 of 2)

- [Max-min Learning of Approximate Weight Matrices from Fuzzy Data](https://mlsanity.com/paper/2301.06141/) (2023)
- [Chebyshev distances associated to the second members of systems of Max-product/Lukasiewicz Fuzzy relational equations](https://mlsanity.com/paper/2302.08554/) (2023)

## Abstract (arXiv)

In this article, we study the inconsistency of a system of max-T fuzzy relational equations of the form A BoxTmax x = b, where T is a t-norm among min, the product or Lukasiewicz's t-norm. For an inconsistent max-T system, we directly construct a canonical maximal consistent subsystem (w.r.t the inclusion order). The main tool used to obtain it is the analytical formula which compute the Chebyshev distance Delta = infc ∈ C Vert b - c Vert associated to the inconsistent max-T system, where C is the set of second members of consistent systems defined with the same matrix A. Based on the same analytical formula, we give, for an inconsistent max-min system, an efficient method to obtain all its consistent subsystems, and we show how to iteratively get all its maximal consistent subsystems.