  Let $H$ be a commutative multiplicative hyperring and $\alpha, \beta \in
\mathbb{Z}^+$. A proper hyperideal $P$ of $H$ is called (weakly)
$(\alpha,\beta)$-prime if $x^\alpha \circ y \subseteq P$ for $x,y \in H$
implies $x^\beta \subseteq P$ or $y \in P$. In this paper, we aim to
investigate (weakly) $(\alpha,\beta)$-prime hyperideals and then we present
some properties of them.
