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

• 作者: Nisar Hundewale S. E. Alam Sultan Aljahdali
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: (m n)-Semihyperring Hyperoperation Hyperideal HOMOMORPHISM Congruence Relation FUZZY (m
• 年，卷（期）: 2013,（1）
• 页码范围: 73-79
• 页数: 7页
• 分类号: O1

摘要

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.