A metaheuristic approach to improve consistency of the pairwise matrix in AHP

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dc.citation.epage1173
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage1164
dc.contributor.affiliationУніверситет Мулая Ісмаїла
dc.contributor.affiliationУніверситет Абдельмалека Ессааді
dc.contributor.affiliationMoulay Ismail University
dc.contributor.affiliationAbdelmalek Essaadi University
dc.contributor.authorТаяні, З.
dc.contributor.authorТаяні, К.
dc.contributor.authorХаттабі, І.
dc.contributor.authorСаббане, М.
dc.contributor.authorTajani, Z.
dc.contributor.authorTajani, C.
dc.contributor.authorKhattabi, I.
dc.contributor.authorSabbane, M.
dc.coverage.placenameЛьвів
dc.date.accessioned2025-03-10T09:21:55Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ цій статті ми зацікавлені в модифікації неузгодженої матриці парного порівняння, яка є критичним кроком у методології AHP, де особи, які приймають рішення, мають покращити узгодженість шляхом перегляду процесу. З цією метою пропонується покращений генетичний алгоритм (GA), щоб дозволити особам, які приймають рішення, знаходити відповідну матрицю та коригувати узгодженість свого судження без втрати вихідної матриці порівняння. Числові результати з матрицями різних розмірів, узятих випадково, виявляють ефективність цієї стратегії для покращення та визначення узгодженості попарної матриці, що означає, що GA є дуже хорошим інструментом для створення узгоджених матриць попарного порівняння з різною кількістю критеріїв.
dc.description.abstractIn this paper, we are interested in modifying inconsistent pairwise comparison matrix which is a critical step in the AHP methodology, where decision makers have to improve the consistency by revising the process. To this end, we propose an improved genetic algorithm (GA) to allow decision makers to find an appropriate matrix and adjust the consistency of their judgment without loss of original comparison matrix. Numerical results with different dimensions of matrices taken randomly show the effectiveness of these strategy to improve and identify the consistency of pairwise matrix which mean that GAs are a very good tool to generate the consistent pairwise comparison matrices with different number of criteria.
dc.format.extent1164-1173
dc.format.pages10
dc.identifier.citationA metaheuristic approach to improve consistency of the pairwise matrix in AHP / Z. Tajani, C. Tajani, I. Khattabi, M. Sabbane // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1164–1173.
dc.identifier.citationenA metaheuristic approach to improve consistency of the pairwise matrix in AHP / Z. Tajani, C. Tajani, I. Khattabi, M. Sabbane // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1164–1173.
dc.identifier.doidoi.org/10.23939/mmc2023.04.1164
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64068
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 4 (10), 2023
dc.relation.references[1] Saaty T. L. The Analytic Hierarchy Process. McGraw-Hill, New York (1980).
dc.relation.references[2] Saaty T. L. Homogeneity and clustering in AHP ensures the validity of the scale. European Journal of Operational Research. 72 (3), 598–601 (1994).
dc.relation.references[3] Breaz R. E., Bologa O., Racz S. G. Selecting industrial robots for milling applications using AHP. Procedia Computer Science. 122, 346–353 (2017).
dc.relation.references[4] Greiner M. A., Fowler J. O., Shunk D. L., Carlyle W. M., McNutt R. T. A hybrid approach using the analytic hierarchy process and integer programming to screen weapon systems projects. IEEE Transactions on Engineering Management. 50 (2), 192–203 (2003).
dc.relation.references[5] Vaidya O. S., Kumar S. Analytic hierarchy process: An overview of applications. European Journal of Operational Research. 169 (1), 1–29 (2006).
dc.relation.references[6] Lance E. F., Verdini W. A. A consistency test for AHP decision makers. Decision Sciences. 20 (3), 575–590 (1989).
dc.relation.references[7] Murphy C. K. Limits on the Analytic Hierarchy Process from its consistency index. European Journal of Operational Research. 65 (1), 138–139 (1993).
dc.relation.references[8] Saaty T. L. Some mathematical concepts of the analytic hierarchy process. Behaviormetrika. 18 (29), 1–9 (1991).
dc.relation.references[9] Ergu D., Kou G., Peng Y., Shi Y. A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP. European Journal of Operational Research. 213 (1), 246–259 (2011).
dc.relation.references[10] Cao D., Leung L. C., Law J. S. Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach. Decision Support Systems. 44 (4), 944–953 (2008).
dc.relation.references[11] Linares P. Are inconsistent decisions better? An experiment with pairwise comparisons. European Journal of Operational Research. 193 (2), 492–498 (2009).
dc.relation.references[12] Saaty T. L. Decision-making with the AHP: Why is the principal eigenvector necessary. European Journal of Operational Research. 145 (1), 85–91 (2003).
dc.relation.references[13] Goldberg D. E. Genetic Algorithm in Search, Optimisation and Machine Learning. Addison-Wesley, Reading (1989).
dc.relation.references[14] Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin (1996).
dc.relation.references[15] Mera N. S., Elliott L., Ingham D. B. A Real Coded Genetic Algorithm Approach for Detection of Subsurface Isotropic and Anisotropic Inclusions. Inverse Problems in Engineering. 11 (2), 157–173 (2003).
dc.relation.references[16] Jouilik B., Tajani C., Daoudi J., Abouchabaka J. Numerical Optimization Algorithm Based On Genetic Algorithm For A Data Completion Problem. TWMS Journal of Applied and Engineering Mathematics. 13 (1), 86–97 (2023).
dc.relation.references[17] Costa J. F. D. S. A Genetic Algorithm to Obtain Consistency in Analytic Hierarchy Process. Brazilian Journal of Operations & Production Management. 8 (1), 55–64 (2011).
dc.relation.references[18] Fei L., Guangzhou Z. Study of genetic algorithm with reinforcement learning to solve the TSP. Expert Systems with Applications. 36 (3), 6995–7001 (2009).
dc.relation.referencesen[1] Saaty T. L. The Analytic Hierarchy Process. McGraw-Hill, New York (1980).
dc.relation.referencesen[2] Saaty T. L. Homogeneity and clustering in AHP ensures the validity of the scale. European Journal of Operational Research. 72 (3), 598–601 (1994).
dc.relation.referencesen[3] Breaz R. E., Bologa O., Racz S. G. Selecting industrial robots for milling applications using AHP. Procedia Computer Science. 122, 346–353 (2017).
dc.relation.referencesen[4] Greiner M. A., Fowler J. O., Shunk D. L., Carlyle W. M., McNutt R. T. A hybrid approach using the analytic hierarchy process and integer programming to screen weapon systems projects. IEEE Transactions on Engineering Management. 50 (2), 192–203 (2003).
dc.relation.referencesen[5] Vaidya O. S., Kumar S. Analytic hierarchy process: An overview of applications. European Journal of Operational Research. 169 (1), 1–29 (2006).
dc.relation.referencesen[6] Lance E. F., Verdini W. A. A consistency test for AHP decision makers. Decision Sciences. 20 (3), 575–590 (1989).
dc.relation.referencesen[7] Murphy C. K. Limits on the Analytic Hierarchy Process from its consistency index. European Journal of Operational Research. 65 (1), 138–139 (1993).
dc.relation.referencesen[8] Saaty T. L. Some mathematical concepts of the analytic hierarchy process. Behaviormetrika. 18 (29), 1–9 (1991).
dc.relation.referencesen[9] Ergu D., Kou G., Peng Y., Shi Y. A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP. European Journal of Operational Research. 213 (1), 246–259 (2011).
dc.relation.referencesen[10] Cao D., Leung L. C., Law J. S. Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach. Decision Support Systems. 44 (4), 944–953 (2008).
dc.relation.referencesen[11] Linares P. Are inconsistent decisions better? An experiment with pairwise comparisons. European Journal of Operational Research. 193 (2), 492–498 (2009).
dc.relation.referencesen[12] Saaty T. L. Decision-making with the AHP: Why is the principal eigenvector necessary. European Journal of Operational Research. 145 (1), 85–91 (2003).
dc.relation.referencesen[13] Goldberg D. E. Genetic Algorithm in Search, Optimisation and Machine Learning. Addison-Wesley, Reading (1989).
dc.relation.referencesen[14] Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin (1996).
dc.relation.referencesen[15] Mera N. S., Elliott L., Ingham D. B. A Real Coded Genetic Algorithm Approach for Detection of Subsurface Isotropic and Anisotropic Inclusions. Inverse Problems in Engineering. 11 (2), 157–173 (2003).
dc.relation.referencesen[16] Jouilik B., Tajani C., Daoudi J., Abouchabaka J. Numerical Optimization Algorithm Based On Genetic Algorithm For A Data Completion Problem. TWMS Journal of Applied and Engineering Mathematics. 13 (1), 86–97 (2023).
dc.relation.referencesen[17] Costa J. F. D. S. A Genetic Algorithm to Obtain Consistency in Analytic Hierarchy Process. Brazilian Journal of Operations & Production Management. 8 (1), 55–64 (2011).
dc.relation.referencesen[18] Fei L., Guangzhou Z. Study of genetic algorithm with reinforcement learning to solve the TSP. Expert Systems with Applications. 36 (3), 6995–7001 (2009).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectгенетичний алгоритм
dc.subjectпопарна матриця
dc.subjectаналітичний процес ієрархії
dc.subjectтеорія прийняття рішень
dc.subjectпослідовність
dc.subjectgenetic algorithm
dc.subjectpairwise matrix
dc.subjectanalytic hierarchy process
dc.subjectdecision theory
dc.subjectconsistency
dc.titleA metaheuristic approach to improve consistency of the pairwise matrix in AHP
dc.title.alternativeМетаевристичний підхід для покращення узгодженості парної матриці в AHP
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 4