The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups

Abstract

We introduce the notion of hypergroupoids $(H\text{Bin}\left(X\right),\square )$, and show that $(H\text{Bin}(X),\square )$ is a super-semigroup of the semigroup $(\text{Bin}(X),\square )$ via the identification $x\leftrightarrow \{x\}$. We prove that $(H\text{Bi}{\text{n}}^{*}(X),\ominus ,[\varnothing ])$ is a $BCK$-algebra, and obtain several properties of $(H\text{Bi}{\text{n}}^{*}(X),\square )$.