×

An interactive approach to determine the elements of a pairwise comparison matrix. (English) Zbl 07061318

Summary: The elicitation process, which provides initial data for further analysis in various decision making problems, can influence the final result (preference scores, weights). The elicitation process is crucial for getting consistent, near-consistent or inconsistent PCM. Decision support systems apply different approaches in practice. This paper aims at investigating two questions. Correction methods are interpreted and analyzed from the viewpoints of their philosophy and techniques to decrease the degree of inconsistency. On the other hand improving consistency in real-world decision problems is not possible without additional information from the decision maker. The proposed interactive method can be applied for individual decision making problems with verbal scale. The involvement of the decision maker and a heuristic rule can ensure that the process either provides a near-consistent and error-free PCM or demonstrates the inability of the decision maker to reach that goal.

MSC:

90Bxx Operations research and management science
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bana e. Costa, CA; Vansnick, JC, A critical analysis of the eigenvalue method used to derive priorities in AHP, Eur J Oper Res, 187, 1422-1428, (2008) · Zbl 1137.91350
[2] Belton, V.; Gear, T., On a short-coming of Saaty’s method of analytic hierarchies, Omega, 11, 228-230, (1983)
[3] Bozóki, S.; Rapcsák, T., On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices, J Global Optim, 42, 157-175, (2008) · Zbl 1177.90205
[4] Bozóki, S.; Fülöp, J.; Rónyai, L., On optimal completion of incomplete pairwise comparison matrices, Math Comput Model, 52, 318-333, (2010) · Zbl 1201.15012
[5] Bozóki, S.; Fülöp, J.; Poesz, A., On pairwise comparison matrices that can be made consistent by the modification of a few elements, CEJOR, 19, 157-175, (2011) · Zbl 1213.90132
[6] Bozóki, S.; Fülöp, J.; Poesz, A., On reducing inconsistency of pairwise comparison matrices below an acceptance threshold, CEJOR, 23, 849-866, (2015) · Zbl 1339.91032
[7] Brunelli M (2015) Introduction to analytic hierarchy process. Springer, Berlin · Zbl 1309.91006
[8] Brunelli, M.; Fedrizzi, M., Axiomatic properties of inconsistency indices for pairwise comparisons, J Oper Res Soc, 66, 1-15, (2015)
[9] Cao, D.; Leung, LC; Law, JS, Modifying inconsistent comparison matrix in analytic hierarchy process: a heuristic approach, Decis Support Syst, 44, 944-953, (2008)
[10] Choo, EU; Wedley, WC, A common framework for deriving preference values from pairwise comparison matrices, Comput Oper Res, 31, 893-908, (2004) · Zbl 1043.62063
[11] Condorcet M (1785) Essai sur l’Application de l’Analyse à la Probabilité des Décisions Rendues á la Pluralité des Voix, Paris
[12] Ergu, D.; Kou, G.; Peng, Y.; Shi, Y., A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP, Eur J Oper Res, 213, 246-259, (2011) · Zbl 1237.90220
[13] Gaul, W.; Gastes, D., A note on consistency improvements of AHP paired comparison data, Adv Data Anal Classif, 6, 289-302, (2012) · Zbl 1254.90082
[14] Gehrlein WV (2006) Condorcet’s paradox. Springer, Berlin · Zbl 1122.91027
[15] González-Pachón, J.; Romero, C., A method for dealing with inconsistencies in pairwise comparisons, Eur J Oper Res, 158, 351-361, (2004) · Zbl 1067.90070
[16] Harker, PT, Incomplete pairwise comparisons in the analytic hierarchy process, Math Model, 9, 837-848, (1987)
[17] Ishizaka, A.; Lustin, M., An expert module to improve the consistency of AHP matrices, Int Trans Oper Res, 11, 97-105, (2004) · Zbl 1057.90026
[18] Karapetrovic, S.; Rosenbloom, ES, A quality control approach to consistency paradoxes in AHP, Eur J Oper Res, 119, 704-718, (1999) · Zbl 0938.91015
[19] Kéri, G., On qualitatively consistent, transitive and contradictory judgment matrices emerging from multiattribute decision procedures, CEJOR, 19, 215-224, (2011) · Zbl 1213.90139
[20] Koczkodaj, WW, A new definition of consistency of pairwise comparisons, Math Comput Model, 8, 79-84, (1993) · Zbl 0804.92029
[21] Kou, G.; Ergu, D.; Shang, J., Enhancing data consistency in decision matrix: adapting Hadamard model to mitigate judgment contradiction, Eur J Oper Res, 236, 261-271, (2014) · Zbl 1338.91057
[22] Kwiesielewicz, M.; Uden, E., Inconsistent judgments in pairwise comparison method in the AHP, Comput Oper Res, 31, 713-719, (2004) · Zbl 1048.90121
[23] Lin, C., A revised framework for deriving preference values from pairwise comparison matrices, Eur J Oper Res, 176, 1145-1150, (2007) · Zbl 1110.90052
[24] Miller, GA, The magical number seven, plus or minus two: some limits on our capacity for processing information, Psychol Rev, 63, 81-97, (1956)
[25] Murphy, CK, Limits on the analytic hierarchy process from its inconsistency index, Eur J Oper Res, 65, 138-139, (1993) · Zbl 0775.90009
[26] Saaty, T., A scaling method for priorities in hierarchical structures, J Math Psychol, 15, 234-281, (1977) · Zbl 0372.62084
[27] Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
[28] Saaty, TL, Decision making with the AHP: why is the principal eigenvector necessary, Eur J Oper Res, 145, 85-91, (2003) · Zbl 1012.90015
[29] Siraj, S.; Mikhailov, L.; Keane, J., A heuristic method to rectify intransitive judgments in pairwise comparison matrices, Eur J Oper Res, 216, 420-428, (2012) · Zbl 1237.90121
[30] Siraj, S.; Mikhailov, L.; Keane, J., Contribution of individual judgments toward inconsistency in pairwise comparisons, Eur J Oper Res, 242, 557-567, (2015) · Zbl 1341.90073
[31] Temesi, J., Pairwise comparison matrices and the error-free property of the decision maker, CEJOR, 19, 239-249, (2011) · Zbl 1213.90144
[32] Temesi, J., (In Hungarian) Determining the elements of a pairwise comparison matrix in case of verbal scale, Szigma, 68, 111-131, (2017)
[33] Xu, ZS; Wei, CP, A consistency improving method in the analytic hierarchy process, Eur J Oper Res, 116, 443-449, (1999) · Zbl 1009.90513
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.