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Triple perturbed consistent matrix and the efficiency of its principal right eigenvector

2024-07Artigo científico Acesso aberto
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dc.contributor.authorFernandes, Rosário
dc.contributor.authorPalheira, Susana
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblElsevier
dc.date.accessioned2025-02-12T21:18:47Z
dc.date.available2025-02-12T21:18:47Z
dc.date.issued2024-07
dc.descriptionPublisher Copyright: © 2024 The Author(s)
dc.description.abstractLet A be a pairwise comparison matrix obtained from a consistent one by perturbing three entries above the main diagonal, x,y,z, and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing the three perturbed entries and not containing a diagonal entry. In this paper we describe the relations among x,y,z with which A always has its principal right eigenvector efficient. Previously, and only for a few cases of this problem, R. Fernandes and S. Furtado (2022) proved the efficiency of the principal right eigenvector of A. In this paper, we continue to use the strong connectivity of a certain digraph associated with A and its principal right eigenvector to characterize the vector efficiency. For completeness, we show that the existence of a sink in this digraph is equivalent to the inefficiency of the principal right eigenvector of A.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent537193
dc.identifier.doi10.1016/j.ijar.2024.109204
dc.identifier.issn0888-613X
dc.identifier.otherPURE: 107371818
dc.identifier.otherPURE UUID: 2402b0fa-7924-49fb-8e98-3c2dc018edc7
dc.identifier.otherScopus: 85190848216
dc.identifier.otherORCID: /0000-0003-2695-9079/work/177968420
dc.identifier.urihttp://hdl.handle.net/10362/178919
dc.identifier.urlhttps://www.scopus.com/pages/publications/85190848216
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT
dc.subjectConsistent matrix
dc.subjectDecision processes
dc.subjectPairwise comparison matrix
dc.subjectPrincipal eigenvector efficiency
dc.subjectStrongly connected digraph
dc.subjectSoftware
dc.subjectTheoretical Computer Science
dc.subjectApplied Mathematics
dc.subjectArtificial Intelligence
dc.titleTriple perturbed consistent matrix and the efficiency of its principal right eigenvectoren
dc.typejournal article
degois.publication.titleInternational Journal of Approximate Reasoning
degois.publication.volume170
dspace.entity.typePublication
oaire.awardNumberUIDB/00297/2020
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT
oaire.fundingStreamConcurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublication6d719021-6aee-40c1-a930-d811c01c997d
relation.isProjectOfPublication.latestForDiscovery6d719021-6aee-40c1-a930-d811c01c997d

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