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

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 (2...

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Main Authors:	Syed Eqbal Alam, Shrisha Rao, Bijan Davvaz
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2013/482391

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spelling	doaj-052170d23a37450b8d9d9176fab84d072020-11-24T23:19:38ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/482391482391(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of SystemsSyed Eqbal Alam0Shrisha Rao1Bijan Davvaz2College of Computers and Information Technology, Taif University, Taif 21974, Saudi ArabiaIIIT-Bangalore, Bangalore 560 100, IndiaDepartment of Mathematics, Yazd University, Yazd, IranWe 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.http://dx.doi.org/10.1155/2013/482391
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Syed Eqbal Alam Shrisha Rao Bijan Davvaz
spellingShingle	Syed Eqbal Alam Shrisha Rao Bijan Davvaz (m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems Journal of Applied Mathematics
author_facet	Syed Eqbal Alam Shrisha Rao Bijan Davvaz
author_sort	Syed Eqbal Alam
title	(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems
title_short	(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems
title_full	(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems
title_fullStr	(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems
title_full_unstemmed	(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems
title_sort	(m,n)-semirings and a generalized fault-tolerance algebra of systems
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2013-01-01
description	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.
url	http://dx.doi.org/10.1155/2013/482391
work_keys_str_mv	AT syedeqbalalam mnsemiringsandageneralizedfaulttolerancealgebraofsystems AT shrisharao mnsemiringsandageneralizedfaulttolerancealgebraofsystems AT bijandavvaz mnsemiringsandageneralizedfaulttolerancealgebraofsystems
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(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems

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