An Algebra of Fuzzy (m, n)-Semihyperrings

S. E. Alam, Sultan Aljahdali, Nisar Hundewale

College of Computers and Information Technology, Taif University, Taif, KSA.

DOI: 10.4236/ajcm.2013.31012                

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.

Keywords

(m, n)-Semihyperring; Hyperoperation; Hyperideal; Homomorphism; Congruence Relation; Fuzzy (m, n)-Semihyperring

Conflicts of Interest

The authors declare no conflicts of interest.

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