An Algebra of Fuzzy (m, n)-Semihyperrings

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semi-hyperring. 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, congru-ence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congru-ence relation, quotient (m, n)-semihyperring, etc. and prove these theorems. We further extend it to introduce the rela-tionship 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)-semihyper-rings