Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bana e Costa CA, Vansnick JC (2008) A critical analysis of the eigenvalue method used to derive priorities in AHP. Eur J Oper Res 187:1422–1428
Belton V, Gear T (1983) On a short-coming of Saaty’s method of analytic hierarchies. Omega 11(3):228–230
Bozóki S, Rapcsák T (2008) On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. J Global Optim 42(2):157–175
Bozóki S, Fülöp J, Rónyai L (2010) On optimal completion of incomplete pairwise comparison matrices. Math Comput Model 52(1–2):318–333
Bozóki S, Fülöp J, Poesz A (2011) On pairwise comparison matrices that can be made consistent by the modification of a few elements. CEJOR 19(2):157–175
Bozóki S, Fülöp J, Poesz A (2015) On reducing inconsistency of pairwise comparison matrices below an acceptance threshold. CEJOR 23(4):849–866
Brunelli M (2015) Introduction to analytic hierarchy process. Springer, Berlin
Brunelli M, Fedrizzi M (2015) Axiomatic properties of inconsistency indices for pairwise comparisons. J Oper Res Soc 66(1):1–15
Cao D, Leung LC, Law JS (2008) Modifying inconsistent comparison matrix in analytic hierarchy process: a heuristic approach. Decis Support Syst 44(4):944–953
Choo EU, Wedley WC (2004) A common framework for deriving preference values from pairwise comparison matrices. Comput Oper Res 31:893–908
Condorcet M (1785) Essai sur l'Application de l'Analyse à la Probabilité des Décisions Rendues á la Pluralité des Voix, Paris
Ergu D, Kou G, Peng Y, Shi Y (2011) A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP. Eur J Oper Res 213(1):246–259
Gaul W, Gastes D (2012) A note on consistency improvements of AHP paired comparison data. Adv Data Anal Classif 6:289–302
Gehrlein WV (2006) Condorcet’s paradox. Springer, Berlin
González-Pachón J, Romero C (2004) A method for dealing with inconsistencies in pairwise comparisons. Eur J Oper Res 158:351–361
Harker PT (1987) Incomplete pairwise comparisons in the analytic hierarchy process. Math Model 9(11):837–848
Ishizaka A, Lustin M (2004) An expert module to improve the consistency of AHP matrices. Int Trans Oper Res 11:97–105
Karapetrovic S, Rosenbloom ES (1999) A quality control approach to consistency paradoxes in AHP. Eur J Oper Res 119(3):704–718
Kéri G (2011) On qualitatively consistent, transitive and contradictory judgment matrices emerging from multiattribute decision procedures. CEJOR 19:215–224
Koczkodaj WW (1993) A new definition of consistency of pairwise comparisons. Math Comput Model 8:79–84
Kou G, Ergu D, Shang J (2014) Enhancing data consistency in decision matrix: adapting Hadamard model to mitigate judgment contradiction. Eur J Oper Res 236(1):261–271
Kwiesielewicz M, van Uden E (2004) Inconsistent judgments in pairwise comparison method in the AHP. Comput Oper Res 31:713–719
Lin C (2007) A revised framework for deriving preference values from pairwise comparison matrices. Eur J Oper Res 176(2):1145–1150
Miller GA (1956) The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol Rev 63:81–97
Murphy CK (1993) Limits on the analytic hierarchy process from its inconsistency index. Eur J Oper Res 65:138–139
Saaty T (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
Saaty TL (2003) Decision making with the AHP: why is the principal eigenvector necessary. Eur J Oper Res 145(1):85–91
Siraj S, Mikhailov L, Keane J (2012) A heuristic method to rectify intransitive judgments in pairwise comparison matrices. Eur J Oper Res 216:420–428
Siraj S, Mikhailov L, Keane J (2015) Contribution of individual judgments toward inconsistency in pairwise comparisons. Eur J Oper Res 242:557–567
Temesi J (2011) Pairwise comparison matrices and the error-free property of the decision maker. CEJOR 19(2):239–249
Temesi J (2017) (In Hungarian) Determining the elements of a pairwise comparison matrix in case of verbal scale. Szigma 68(3–4):111–131
Xu ZS, Wei CP (1999) A consistency improving method in the analytic hierarchy process. Eur J Oper Res 116(2):443–449
Author information
Authors and Affiliations
Corresponding author
Additional information
The research was supported by the Hungarian National Research Fund, Grant K 111797.
Rights and permissions
About this article
Cite this article
Temesi, J. An interactive approach to determine the elements of a pairwise comparison matrix. Cent Eur J Oper Res 27, 533–549 (2019). https://doi.org/10.1007/s10100-018-0539-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-018-0539-6