# Chebyshev distances associated to the second members of systems of Max-product/Lukasiewicz Fuzzy relational equations

arXiv: https://arxiv.org/abs/2302.08554 · HTML: https://mlsanity.com/paper/2302.08554/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 22 references that are in the map.
- First posted on arXiv 30 Jan 2023.

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

- [Max-min Learning of Approximate Weight Matrices from Fuzzy Data](https://mlsanity.com/paper/2301.06141/) (2023)

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

- [Handling the inconsistency of systems of minrightarrow fuzzy relational equations](https://mlsanity.com/paper/2308.12385/) (2023)
- [Maximal Consistent Subsystems of Max-T Fuzzy Relational Equations](https://mlsanity.com/paper/2311.03059/) (2023)

## Abstract (arXiv)

In this article, we study the inconsistency of a system of max-product fuzzy relational equations and of a system of max-Lukasiewicz fuzzy relational equations. For a system of max-min fuzzy relational equations A Boxminmax x = b and using the L_∞ norm, (Baaj, 2023) showed that the Chebyshev distance Delta = infc ∈ C Vert b - c Vert, where C is the set of second members of consistent systems defined with the same matrix A, can be computed by an explicit analytical formula according to the components of the matrix A and its second member b. In this article, we give analytical formulas analogous to that of (Baaj, 2023) to compute the Chebyshev distance associated to the second member of a system of max-product fuzzy relational equations and that associated to the second member of a system of max-Lukasiewicz fuzzy relational equations.