Achieving matrix consistency in AHP through linearization

Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pair-wise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent - and sometimes t...

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Autores: Benítez López, Julio|||0000-0002-3222-3036, Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226, Delgado Galván, Xitlali Virginia, Pérez García, Rafael
Tipo de recurso: artículo
Fecha de publicación:2011
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:10251/52706
Acceso en línea:https://riunet.upv.es/handle/10251/52706
Access Level:acceso abierto
Palabra clave:Analytic Hierarchy Process
Decision-making
Linearization
Leakage management
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
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spelling Achieving matrix consistency in AHP through linearizationBenítez López, Julio|||0000-0002-3222-3036Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226Delgado Galván, Xitlali VirginiaPérez García, RafaelAnalytic Hierarchy ProcessDecision-makingLinearizationLeakage managementMATEMATICA APLICADAINGENIERIA HIDRAULICAMatrices used in the analytic hierarchy process (AHP) compile expert knowledge as pair-wise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent - and sometimes the level of consistency may be unacceptable. Different methods have been used in the literature to achieve consistency for an inconsistent matrix. In this paper we use a linearization technique that provides the closest consistent matrix to a given inconsistent matrix using orthogonal projection in a linear space. As a result, consistency can be achieved in a closed form. This is simpler and cheaper than for methods relying on optimisation, which are iterative by nature. We apply the process to a real-world decision-making problem in an important industrial context, namely, management of water supply systems regarding leakage policies - an aspect of water management to which great sums of money are devoted every year worldwide. (C) 2011 Elsevier Inc. All rights reserved.This work has been performed under 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 Riunet20112011-09-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/52706reponame: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:10251/527062026-06-13T07:49:27Z
dc.title.none.fl_str_mv Achieving matrix consistency in AHP through linearization
title Achieving matrix consistency in AHP through linearization
spellingShingle Achieving matrix consistency in AHP through linearization
Benítez López, Julio|||0000-0002-3222-3036
Analytic Hierarchy Process
Decision-making
Linearization
Leakage management
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
title_short Achieving matrix consistency in AHP through linearization
title_full Achieving matrix consistency in AHP through linearization
title_fullStr Achieving matrix consistency in AHP through linearization
title_full_unstemmed Achieving matrix consistency in AHP through linearization
title_sort Achieving matrix consistency in AHP through linearization
dc.creator.none.fl_str_mv Benítez López, Julio|||0000-0002-3222-3036
Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Delgado Galván, Xitlali Virginia
Pérez García, Rafael
author Benítez López, Julio|||0000-0002-3222-3036
author_facet Benítez López, Julio|||0000-0002-3222-3036
Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Delgado Galván, Xitlali Virginia
Pérez García, Rafael
author_role author
author2 Izquierdo Sebastián, Joaquín|||0000-0002-6625-7226
Delgado Galván, Xitlali Virginia
Pérez García, Rafael
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
Leakage management
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
topic Analytic Hierarchy Process
Decision-making
Linearization
Leakage management
MATEMATICA APLICADA
INGENIERIA HIDRAULICA
description Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pair-wise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent - and sometimes the level of consistency may be unacceptable. Different methods have been used in the literature to achieve consistency for an inconsistent matrix. In this paper we use a linearization technique that provides the closest consistent matrix to a given inconsistent matrix using orthogonal projection in a linear space. As a result, consistency can be achieved in a closed form. This is simpler and cheaper than for methods relying on optimisation, which are iterative by nature. We apply the process to a real-world decision-making problem in an important industrial context, namely, management of water supply systems regarding leakage policies - an aspect of water management to which great sums of money are devoted every year worldwide. (C) 2011 Elsevier Inc. All rights reserved.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-09-01
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/10251/52706
url https://riunet.upv.es/handle/10251/52706
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
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