%0 Journal Article %T An Algebra of Fuzzy (<i>m</i>, <i>n</i>)-Semihyperrings %A S. E. Alam %A Sultan Aljahdali %A Nisar Hundewale %J American Journal of Computational Mathematics %P 73-79 %@ 2161-1211 %D 2013 %I Scientific Research Publishing %R 10.4236/ajcm.2013.31012 %X

We propose a new class of algebraic structure named as (m, n)-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