TITLE:
An Algebra of Fuzzy (m, n)-Semihyperrings
AUTHORS:
S. E. Alam, Sultan Aljahdali, Nisar Hundewale
KEYWORDS:
(m, n)-Semihyperring; Hyperoperation; Hyperideal; Homomorphism; Congruence Relation; Fuzzy (m, n)-Semihyperring
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.1,
March
29,
2013
ABSTRACT:
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, 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.