# Reducing fuzzy relation equations via concept lattices

arXiv: https://arxiv.org/abs/2410.05728 · HTML: https://mlsanity.com/paper/2410.05728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 44 references that are in the map.
- First posted on arXiv 8 Oct 2024.

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

- [Bipolar fuzzy relation equations systems based on the product t-norm](https://mlsanity.com/paper/2410.02816/) (2024)

## Abstract (arXiv)

This paper has taken into advantage the relationship between Fuzzy Relation Equations (FRE) and Concept Lattices in order to introduce a procedure to reduce a FRE, without losing information. Specifically, attribute reduction theory in property-oriented and object-oriented concept lattices has been considered in order to present a mechanism for detecting redundant equations. As a first consequence, the computation of the whole solution set of a solvable FRE is reduced. Moreover, we will also introduce a novel method for computing approximate solutions of unsolvable FRE related to a (real) dataset with uncertainty/imprecision data.