Abstract
A review of contemporary literature devoted to decision making support systems draws attention to the Analytic Hierarchy Process (AHP). At the core of the AHP are various prioritization procedures which elicit priorities for alternative solutions for complex decisional problems. Certainly, the procedures coincide when decision makers’ preferences of alternative solutions are cardinally transitive, otherwise the results differ. This is why consistency measurement of human judgments is so important. It has been scientifically proven that a high inconsistency of decision makers’ preferences concerning alternative solutions of decisional problems may lead to fallacious choices. Research verifies the thesis that consistency measures derived from different prioritization procedures are interrelated. It turns out that one of the independent consistency measures is extremely closely related to the consistency index embedded in original approach of the AHP. The main objective of this study is realized through the novel and sophisticated simulation algorithm designed for the AHP and executed within its exemplary decisional framework for three levels. The outcome of the research proves that consistency can be measured in various ways, but recently devised concepts can indicate better solutions as a result of significantly improved methodology.
Similar content being viewed by others
References
Aguarón, J., Escobar, M. T., & Moreno-Jiménez, J. M. (2014). The precise consistency consensus matrix in a local AHP-group decision making context. Annals of Operations Research, 1–15. doi:10.1007/s10479-014-1576-8.
Aguaron, J., & Moreno-Jimenez, J. M. (2003). The geometric consistency index: Approximated thresholds. European Journal of Operational Research, 147, 137–145. doi:10.1016/S0377-2217(02)00255-2.
Barzilai, J. (2005). Measurement and preference function modeling. International Transactions in Operational Research, 12, 173–183. doi:10.1111/j.1475-3995.2005.00496.x.
Basak, I. (1998). Comparison of statistical procedures in analytic hierarchy process using a ranking test. Mathematical and computer modelling, 28, 105–118. doi:10.1016/S0895-7177(98)00174-5.
Bana e Costa, C. A., & Vansnick, J. C. (2008). A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research, 187, 1422–1428. doi:10.1016/j.ejor.2006.09.022.
Bozóki, S., Dezső, L., Poesz, A., & Temesi, J. (2013). Analysis of pairwise comparison matrices: An empirical research. Annals of Operations Research, 211(1), 511–528. doi:10.1007/s10479-013-1328-1.
Bozóki, S., & Rapcsák, T. (2008). On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. Journal of Global Optimization, 42, 157–175. doi:10.1007/s10898-007-9236-z.
Brunelli, M., Canal, L., & Fedrizzi, M. (2013). Inconsistency indices for pairwise comparison matrices: A numerical study. Annals of Operations Research, 211(1), 493–509. doi:10.1007/s10479-013-1329-0.
Chen, K., Kou, G., Tarn, J. M., & Song, Y. (2015). Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices. Annals of Operations Research, 1–21. doi:10.1007/s10479-015-1997-z.
Choo, E. U., & Wedley, W. C. (2004). A common framework for deriving preference values from pairwise comparison matrices. Computers and Operations Research, 31, 893–908. doi:10.1016/S0305-0548(03)00042-X.
Crawford, G., & Williams, C. A. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29, 387–405. doi:10.1016/0022-2496(85)90002-1.
Dong, Y., Xu, Y., Li, H., & Dai, M. (2008). A comparative study of the numerical scales and the prioritization methods in AHP. European Journal of Operational Research, 186, 229–242. doi:10.1016/j.ejor.2007.01.044.
Farkas, A. (2007). The analysis of the principal eigenvector of pairwise comparison matrices. Acta Polytechnica Hungarica. 4(2). http://uni-obuda.hu/journal/Farkas_10.pdf.
Grzybowski, A. Z. (2012). Note on a new optimization based approach for estimating priority weights and related consistency index. Expert Systems with Applications, 39, 11699–11708. doi:10.1016/j.eswa.2012.04.051.
Hovanov, N. V., Kolari, J. W., & Sokolov, M. V. (2008). Deriving weights from general pairwise comparison matrices. Mathematical Social Sciences, 55, 205–220. doi:10.1016/j.mathsocsci.2007.07.006.
Kazibudzki, P. T., & Grzybowski, A. Z. (2013). On some advancements within certain multicriteria decision making support methodology. American Journal of Business and Management, 2(2), 143–154. doi:10.11634/216796061302287.
Kazibudzki, P. T. (2012). Note on some revelations in prioritization, theory of choice and decision making support methodology. African Journal of Business Management, 6(48), 11762–11770. doi:10.5897/AJBM12.899.
Koczkodaj, W. W. (1993). A new definition of consistency of pairwise comparisons. Mathematical and Computer Modeling, 18(7), 79–84. doi:10.1016/0895-7177(93)90059-8.
Lin, C. (2007). A revised framework for deriving preference values from pairwise comparison matrices. European Journal of Operational Research, 176, 1145–1150. doi:10.1016/j.ejor.2005.09.022.
Lin, C., Kou, G., & Ergu, D. (2013). An improved statistical approach for consistency test in AHP. Annals of Operations Research, 211(1), 289–299. doi:10.1007/s10479-013-1413-5.
Linares, P., Lumbreras, S., Santamaría, A., & Veiga, A. (2014). How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP. Annals of Operations Research, (pp. 1–18). doi:10.1007/s10479-014-1767-3.
Lipovetsky, S., & Tishler, A. (1997). Interval estimation of priorities in the AHP. European Journal of Operational Research, 114, 153–164. doi:10.1016/S0377-2217(98)00012-5.
Moreno-Jiménez, J. M., Salvador, M., Gargallo, P., & Altuzarra, A. (2014). Systemic decision making in AHP: A Bayesian approach. Annals of Operations Research, (pp. 1–24). doi:10.1007/s10479-014-1637-z.
Pereira, V., & Costa, H. G. (2015). Nonlinear programming applied to the reduction of inconsistency in the AHP method. Annals of Operations Research, 229(1), 635–655. doi:10.1007/s10479-014-1750-z.
Saaty, T. L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.
Saaty, T. L. (1990). How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 48, 9–26. doi:10.1016/0377-2217(90)90057-I.
Xu, Z. S. (2004). Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. International Journal of Approximate Reasoning, 36, 261–270. doi:10.1016/j.ijar.2003.10.011.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kazibudzki, P.T. An examination of performance relations among selected consistency measures for simulated pairwise judgments. Ann Oper Res 244, 525–544 (2016). https://doi.org/10.1007/s10479-016-2131-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-016-2131-6