Abstract: In this paper the concept of the cosets of an anti Lfuzzy
normal subgroup of a group is given. Furthermore, the group
G/A of cosets of an anti L-fuzzy normal subgroup A of a group
G is shown to be isomorphic to a factor group of G in a natural
way. Finally, we prove that if f : G1 -→ G2 is an epimorphism of
groups, then there is a one-to-one order-preserving correspondence
between the anti L-fuzzy normal subgroups of G2 and those of G1
which are constant on the kernel of f.