A hypergroup is a algebraic structure similar to a group, but where the composition operation does not just take two elements to a single product element in the group, but to a subset of elements of the group.
A canonical hypergroup is a set, , equipped with a commutative binary operation,
+ : H \times H \to P^*(H)
taking values in non-empty subsets of , and a zero element , such that
The additive structure underlying a hyperring is a canonical hypergroup. See there for more examples.