(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems

IF 1.2 Q2 MATHEMATICS, APPLIED
Syed Eqbal Alam, Shrisha Rao, B. Davvaz
{"title":"(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems","authors":"Syed Eqbal Alam, Shrisha Rao, B. Davvaz","doi":"10.1155/2013/482391","DOIUrl":null,"url":null,"abstract":"We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/482391","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2013/482391","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 7

Abstract

We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.
(m,n)-半环与系统的广义容错代数
我们提出了一类新的数学结构,称为(m,n)-半环(它推广了通常的半环),并描述了它们的基本性质。对于(m,n)-半环,我们定义了偏序,并推广了同余、同态等概念。根据Rao(2008)的早期工作,我们考虑由几个组件组成的系统,这些组件的故障可能导致它们失效,并将这些系统的集合代数地表示为(m,n)-半环。基于这些组件的特征,我们提出了一种比较两个系统容错行为的形式化方法,使用我们的部分有序(m,n)-半环框架。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信