Abstract
In this work we introduce the notion of fuzzy congruence relation on an nd-groupoid and study conditions on the nd-groupoid that guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.
Acknowledgements
We thank Prof. Dragoş Vaida for his valuable comments on preliminary versions of this article. The authors have been partially supported by projects TIN2006-15455-C03-01, TIN2007-65819 (Science Ministry of Spain) and P06-FQM-02049 (Junta de Andalucía).