  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.
