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 $(m,n)$-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.
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