Chain complex and quotient structure of fuzzy hypergroups

In this paper, we introduce a regular relations on fuzzy hypergroups by sub-fuzzy hypergroup and construct the quotient fuzzy hypergroups by these relations. We consider, when sub-fuzzy hypergroups are normal, the regular relation construct by this sub fuzzy hypergroups is strongly regular. Hence hyperadditions defined by M. Norouzi et. al. on quotient structures are just operations. Also, we define a covariant functor between the fuzzy hypergroups category and the groups category. Moreover, we present some connections between fuzzy hypergroup homomorphisms and hypergroup homomorphisms and group homomorphisms. Also, we define chain complex and homology of chain complex of fuzzy hypergroup category.