Krasner $F^{(m, n)}$-Hyperrings

$\!\!\!\!$ In this paper, the notion of fuzzy $\!$ Krasner $\!(m, n)$-hyperrings ($\!F^{(m, n)}\!$-hyperrings) by using the notion of $F^m$-hyperoperations and $F^n$-operations is introduced and some related properties are investigated. In this regards, relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner $(m, n)$-hyperrings are considered. We shall prove that every Krasner $F^{(m, n)}$-hyperring is extended by a Krasner $F^{(2, n)}$-hyperring. The concepts of normal $F$-hyperideals and homomorphisms of Krasner $F^{(m, n)}$-hyperrings are adopted. Also, the quotient of Krasner $F^{(m, n)}$-hyperrings by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Krasner $F^{(m, n)}$-hyperrings provided the $F$-hyperideals considered in them are normal.