hypersemigroup

hyper- +‎ semigroup

hypersemigroup (plural hypersemigroups)

1. (mathematics) A nonempty set for which the set of all subsets forms a semiring.
   • 2016, Niovi Kehayopulu, “A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets”, in arXiv‎:

     An hypersemigroup ${\displaystyle H}$ is left (resp. right) quasi-regular if and only if, for any fuzzy subset ${\displaystyle f}$ of ${\displaystyle S}$ we have ${\displaystyle f\preceq 1\circ f\circ 1\circ f}$ (resp. ${\displaystyle f\preceq f\circ 1\circ f\circ 1)}$ and it is semisimple if and only if, for any fuzzy subset ${\displaystyle f}$ of ${\displaystyle S}$ we have ${\displaystyle f\preceq 1\circ f\circ 1\circ f\circ 1}$.

• semihypergroup