Abstract
In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if A is any fuzzy AG-subgroup of G, then mu(A)(xy) = mu(A)(yx) for all x, y is an element of G, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number [G : A]. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange's theorem of finite AG-group is also introduced.