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We propose a new class of algebraic structure named as (m, n)</a>-semihyperring which is a generalization of usual 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)-semihyper-rings. </p

An Algebra of Fuzzy (&lt;i&gt;m&lt;/i&gt;, &lt;i&gt;n&lt;/i&gt;)-Semihyperrings

An Algebra of Fuzzy (<i>m</i>, <i>n</i>)-Semihyperrings