Optimal inconsistency repairing of pairwise comparison matrices using integrated linear programming and eigenvector methods

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Zhang, Haiqing ^a   Sekhari, Aicha ^a   Ouzrout, Yacine ^a   Bouras, Abdelaziz ^a,b  

^a University Jean Monnet of Saint Etienne   (France)

^b Qatar University   (Qatar)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ANALYTIC HIERARCHY PROCESS; EXPERIMENTS; HIERARCHICAL SYSTEMS; TREES (MATHEMATICS);

ANALYTIC HIERARCHY PROCESS (AHP); CONSISTENCY REQUIREMENTS; CONSISTENT VALUES; CONVERGENCE RATES; CRITICAL STEPS; DECISION MAKING METHODOLOGY; EIGENVECTOR METHODS; PAIRWISE COMPARISON MATRICES;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84897556557     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/989726     Document Type: Article

References (33)

1. Saaty T. L., The Analytic Hierarchy Process 1980 New York, NY, USA McGraw-Hill
2. Zhang H. Q., Ouzrout Y., Bouras A., Della Selva V., Savino M., Selection of optimal product lifecycle management components based on AHP methodologies. Proceedings of the International Conference on Advanced Logistics and Transport (ICALT '13) May 2013 Sousse, Tunisia 523 528
3. Zhang H. Q., Ouzrout Y., Bouras A., Mazza A., Savino M., PLM components selection based on a maturity assessment and AHP methodology. Proceedings of the International Conference on Product Lifecycle Management Conference (PLM '13) July 2013 Nantes, France
4. Torfi F., Farahani R. Z., Rezapour S., Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives. Applied Soft Computing Journal 2010 10 2 520 528 2-s2.0-70649102118 10.1016/j.asoc.2009.08.021
5. Karapetrovic S., Rosenbloom E. S., A quality control approach to consistency paradoxes in AHP. European Journal of Operational Research 1999 119 3 704 718 2-s2.0-0033347835 10.1016/S0377-2217(98)00334-8 (Pubitemid 30509803)
6. Xu Z. S., Wei C. P., A consistency improving method in the analytic hierarchy process. European Journal of Operational Research 1999 116 2 443 449 2-s2.0-0344672501 10.1016/S0377-2217(98)00109-X
7. Cao D., Leung L. C., Law J. S., Modifying inconsistent comparison matrix in analytic hierarchy process: a heuristic approach. Decision Support Systems 2008 44 4 944 953 2-s2.0-38649113569 10.1016/j.dss.2007.11.002
8. Anholcer M., Algorithm for Deriving Priorities from Inconsistent Pairwise Comparison Matrices 2013
9. Xu Y. J., Wang H. M., Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation. Applied Mathematical Modelling 2013 37 5171 5183
10. Leung L. C., Cao D., On consistency and ranking of alternatives in fuzzy AHP. European Journal of Operational Research 2000 124 1 102 113 2-s2.0-0034230856 10.1016/S0377-2217(99)00118-6
11. Morteza M., Bafandeh A. R., A new method for consistency test in fuzzy AHP. Journal of Intelligent and Fuzzy Systems 2013 25 2 457 461
12. Wang T. C., Chen Y. H., Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Information Sciences 2008 178 19 3755 3765 2-s2.0-46549093655
13. Ramík J., Korviny P., Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets and Systems 2010 161 11 1604 1613 2-s2.0-77949911118 10.1016/j.fss.2009.10.011
14. Bulut E., Duru O., Keçeci T., Yoshida S., Use of consistency index, expert prioritization and direct numerical inputs for generic fuzzy-AHP modeling: a process model for shipping asset management. Expert Systems with Applications 2012 39 2 1911 1923 2-s2.0-80054947843 10.1016/j.eswa.2011.08.056
15. Dopazo E., Lui K., Chouinard S., Guisse J., A parametric model for determining consensus priority vectors from fuzzy comparison matrices. Fuzzy Sets and Systems 2013 10.1016/j.fss.2013.07.022
16. Buckley J. J., Fuzzy hierarchical analysis. Fuzzy Sets and Systems 1985 17 3 233 247 2-s2.0-46549093655
17. Aguarón J., Moreno-Jiménez J. M., The geometric consistency index: approximated thresholds. European Journal of Operational Research 2003 147 1 137 145 2-s2.0-0037449042 10.1016/S0377-2217(02)00255-2
18. Gass S. I., Rapcsák T., Singular value decomposition in AHP. European Journal of Operational Research 2004 154 3 573 584 2-s2.0-0347593843 10.1016/S0377-2217(02)00755-5
19. Stein W. E., Mizzi P. J., The harmonic consistency index for the analytic hierarchy process. European Journal of Operational Research 2007 177 1 488 497 2-s2.0-33750476963 10.1016/j.ejor.2005.10.057 (Pubitemid 44647621)
20. Saaty T. L., Multi-Criteria Decision Making-the Analytical Hierarchy Process 1991 1 Pittsburgh, Pa, USA RWS Publications
21. Dubois D., The role of fuzzy sets in decision sciences: old techniques and new directions. Fuzzy Sets and Systems 2011 184 1 3 28 2-s2.0-80052970862 10.1016/j.fss.2011.06.003
22. Yang M., Khan F. I., Sadiq R., Prioritization of environmental issues in offshore oil and gas operations: a hybrid approach using fuzzy inference system and fuzzy analytic hierarchy process. Process Safety and Environmental Protection 2011 89 1 22 34 2-s2.0-78651248928 10.1016/j.psep.2010.08.006
23. Brunelli M., A note on the article "inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean" Fuzzy Sets and Systems, vol. 161, 1604-1613, 2010. Fuzzy Sets and Systems 2011 176 1 76 78 2-s2.0-79958166659 10.1016/j.fss.2011.03.013
24. Aguarón J., Moreno-Jiménez J. M., The geometric consistency index: approximated thresholds. European Journal of Operational Research 2003 147 137 145
25. Bana e Costa C. A., Vansnick J.-C., A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research 2008 187 3 1422 1428 2-s2.0-36849024019 10.1016/j.ejor.2006.09.022 (Pubitemid 350236646)
26. de Jong P., A statistical approach to Saaty's scaling method for priorities. Journal of Mathematical Psychology 1984 28 4 467 478 2-s2.0-0001270743
27. Saaty T. L., Hu G., Ranking by eigenvector versus other methods in the analytic hierarchy process. Applied Mathematics Letters 1998 11 4 121 125 2-s2.0-0013251599 (Pubitemid 128389782)
28. Saaty T. L., Decision-making with the AHP: why is the principal eigenvector necessary. European Journal of Operational Research 2003 145 1 85 91 2-s2.0-0037448775 10.1016/S0377-2217(02)00227-8
29. Almulhim T. S., Mikhailov L., Xu D.-L., Deriving weights from group fuzzy pairwise comparison judgement matrices. Advances in Information Systems and Technologies 2013 Springer 545 555
30. Mogi W., Izumi-cho N., Shinohara M., Optimum priority weight estimation method for pairwise comparison matrix. Proceedings of the 10th International Symposium on the Analytic Hierarchy/Network Process 2009
31. Crawford G., Williams C., A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology 1985 29 4 387 405 2-s2.0-0001490143
32. Kou G., Ergu D., Peng Y., Shi Y., A new consistency test index for the data in the AHP/ANP. Data Processing for the AHP/ANP 2013 Springer 11 27
33. Winston W. L., Venkataramanan M., Goldberg J. B., Introduction to Mathematical Programming 2003 1 Thomson/Brooks/Cole