(Weakly) $(\alpha ,\beta )$-prime hyperideals in commutative multiplicative hypeering

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.