We introduce the notion of a quotient semigroup S/rho induced by a fuz
zy congruence relation rho on a semigroup S, and give Homomorphism The
orems with respect to the fuzzy congruence. We also introduce the noti
on of an idempotent-separating fuzzy congruence, a group fuzzy congrue
nce on inverse semigroups, and give some of their properties on invers
e semigroups. (C) 1997 Elsevier Science B.V.