L-Multialgebras and P-Fuzzy Congruences of Multialgebras
R. Ameri and I.G. Rosenberg
We define and study L-multialgebra (also called L-hyperalgebras) and fuzzy congruences of multialgebras. First the notion of L-multialgebras is introduced and the notion of P-fuzzy relation on multialgebras is given, where P is any down directed ordered set. These notions will be applied to introduce the notions of P-fuzzy congruences and P-fuzzy strong congruences of multialgebras. Finally, the lattices of P-fuzzy and strong P-fuzzy congruence of multialgebras are constructed and basic properties of these lattices are investigated.
Keywords: multialgebra, compatible and strong compatible relations, congruence lattices, P-fuzzy sets, similarity relation, P-fuzzy relations, P-fuzzy congruences