Fuzzy universal algebras on L-sets

This paper attempts to generalize universal algebras on classical sets to L-sets when L is a GL-quantale. Some basic notions of fuzzy universal algebra on an L-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. L-valued power algebra is also introduced and it is shown there is an onto homomorphism from P(A)/R+ to P(A/R) for any congruence R on L-set A.