Transposition hypergroups and complement hypergroups

Abstract

We introduce the complement of a hyperoperation. We provide an example to reveal that the complement of a transposition hypergroup may be a transposition hypergroup. However, we show that the complement of a hypergroup in general is not a hypergroup. We prove that, under certain condition, the complement of a quasi-hypergroup is a quasihypergroup.

Keywords:

• Quasi-hypergroup
• hypergroup
• hyperoperation