We propose a new class of algebraic structure named as \emph{
(m,n)-semihyperring} which is a generalization of usual \emph{semihyperring}. We define the basic properties of
(m,n)-semihyperring like identity elements, weak distributive
(m,n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient
... [Show full abstract] (m,n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m,n)-semihyperring, etc and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m,n)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m,n)-semihyperrings and the relationship between fuzzy (m,n)-semihyperrings and the usual (m,n)-semihyperrings.