(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

Syed Eqbal Alam; Sultan Aljahdali; Nisar Hundewale

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arXiv · 1511.02773

(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

Syed Eqbal Alam·Sultan Aljahdali·Nisar Hundewale

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Abstract

We propose a new class of algebraic structure named as \emph{$(m,n)$-semihyperring} which is a generalization of usual \emph{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 $(m,n)$-semihyperrings.

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Syed Eqbal Alam, Sultan Aljahdali, Nisar Hundewale. 2015-11-04. (m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings. https://arxiv.org/abs/1511.02773

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