Quasi-order hypergroups, introduced by J. Chvalina, form a subclass of the class of all hypergroups, i.e. structures with one associative hyperoperation fulfilling the reproduction axiom. In this paper a theorem is proved that allows an easy description of all quasi-order hypergroups. The usefulness of this result is shown on new proofs of known results concerning the relation of quasi-order and upper quasi-order hypergroups.
quasi-order hypergroups, order hypergroups
