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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 $(m,n)$-semihyperringlike 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 lemmasand theorems on homomorphism, congruence relation, quotient$(m,n)$-semihyperring, etc and prove these theorems. We further extend it tointroduce the relationship between fuzzy sets and $(m,n)$-semihyperrings andpropose fuzzy hyperideals and homomorphism theorems on fuzzy$(m,n)$-semihyperrings and the relationship between fuzzy$(m,n)$-semihyperrings and the usual $(m,n)$-semihyperrings.

(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings