A simple formula to find the closest consistent matrix to a reciprocal matrix

Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et...

Descripción completa

Detalles Bibliográficos
Autores: Benítez López, Julio|||0000-0002-3222-3036, Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226, Pérez García, Rafael, Ramos Martínez, Eva
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/52709
Acceso en línea:https://riunet.upv.es/handle/10251/52709
Access Level:acceso abierto
Palabra clave:Analytic Hierarchy Process
Decision-making
Linearization
ECOLOGIA
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
id ES_0cd1d992d059fa2c44e71f68309afc7d
oai_identifier_str oai:riunet.upv.es:10251/52709
network_acronym_str ES
network_name_str España
repository_id_str
spelling A simple formula to find the closest consistent matrix to a reciprocal matrixBenítez López, Julio|||0000-0002-3222-3036Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226Pérez García, RafaelRamos Martínez, EvaAnalytic Hierarchy ProcessDecision-makingLinearizationECOLOGIAMATEMATICA APLICADAINGENIERIA HIDRAULICAAchieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. (C) 2014 Elsevier Inc. All rights reserved.This work has been performed with the support of the project IDAWAS, DPI2009-11591 of the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain), with the supplementary support of ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana, and the support given to the first author by the Spanish project MTM2010-18539. The use of English in this paper was revised by John Rawlins; and the revision was funded by the Universitat Politecnica de Valencia, Spain.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarMinisterio de Ciencia e InnovaciónGeneralitat ValencianaUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20142014-08-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/52709reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 DPI2009-11591 Aplicacion De Herramientas Del Analisis Inteligente De Datos En La Gestion Tecnica De Sistemas De Distribucion Y Evacuacion De AguasGeneralitat Valenciana https://doi.org/10.13039/501100003359 ACOMP%2F2010%2F146Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-18539 DISEÑO, ANALISIS Y OPTIMIZACION DE METODOS DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES. APLICACIONES A PROBLEMAS DE VALOR INICIAL Y FLUJO OPTICOopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/527092026-06-13T07:49:27Z
dc.title.none.fl_str_mv A simple formula to find the closest consistent matrix to a reciprocal matrix
title A simple formula to find the closest consistent matrix to a reciprocal matrix
spellingShingle A simple formula to find the closest consistent matrix to a reciprocal matrix
Benítez López, Julio|||0000-0002-3222-3036
Analytic Hierarchy Process
Decision-making
Linearization
ECOLOGIA
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
title_short A simple formula to find the closest consistent matrix to a reciprocal matrix
title_full A simple formula to find the closest consistent matrix to a reciprocal matrix
title_fullStr A simple formula to find the closest consistent matrix to a reciprocal matrix
title_full_unstemmed A simple formula to find the closest consistent matrix to a reciprocal matrix
title_sort A simple formula to find the closest consistent matrix to a reciprocal matrix
dc.creator.none.fl_str_mv Benítez López, Julio|||0000-0002-3222-3036
Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Pérez García, Rafael
Ramos Martínez, Eva
author Benítez López, Julio|||0000-0002-3222-3036
author_facet Benítez López, Julio|||0000-0002-3222-3036
Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Pérez García, Rafael
Ramos Martínez, Eva
author_role author
author2 Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Pérez García, Rafael
Ramos Martínez, Eva
author2_role author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Ministerio de Ciencia e Innovación
Generalitat Valenciana
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Analytic Hierarchy Process
Decision-making
Linearization
ECOLOGIA
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
topic Analytic Hierarchy Process
Decision-making
Linearization
ECOLOGIA
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
description Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. (C) 2014 Elsevier Inc. All rights reserved.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/52709
url https://riunet.upv.es/handle/10251/52709
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 DPI2009-11591 Aplicacion De Herramientas Del Analisis Inteligente De Datos En La Gestion Tecnica De Sistemas De Distribucion Y Evacuacion De Aguas
Generalitat Valenciana https://doi.org/10.13039/501100003359 ACOMP%2F2010%2F146
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-18539 DISEÑO, ANALISIS Y OPTIMIZACION DE METODOS DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES. APLICACIONES A PROBLEMAS DE VALOR INICIAL Y FLUJO OPTICO
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869403305735618560
score 15.300719

Similares en LA Referencia