Pairwise judgments consistency impact on quality of multi-criteria group decision-making with AHP[S1]

dc.contributor.authorKazibudzki, Pawel Tadeusz
dc.contributor.authorKřupka, Jiří
dc.contributor.otherEkonomická fakultacs
dc.date.accessioned2019-11-28T10:20:14Z
dc.date.available2019-11-28T10:20:14Z
dc.description.abstractThe scope of this research encompasses issues associated with group decision making (GDM) as the most challenging process which entails various viewpoints and preferences of individuals that must be taken into consideration and somehow combined into one meaningful outcome. When GDM is taken into consideration, the AHP seems to be a particularly attractive methodology. From the perspective of its applications, an existing research gap has been identified and examined in this research paper. Thus, the inconsistency of judgments impact on priority vector quality has been examined from the perspective of group decision making. Examination results generalize to the synthesized pairwise comparison matrix that is obtained on the basis of individual pairwise comparison matrices for all group members. The examination process has proceeded with the application of Monte Carlo simulations coded and executed in Wolfram Mathematica Software. Having in mind that a consistency index for the PCM denoting group preferences cannot be greater than the consistency index of the most inconsistent individual PCM it became possible to designate the credibility of the priority vector for the group on the basis of the most inconsistent individual PCM. It is emphasized that thus far only a few papers have dealt with the problem concerning the relation between a level of the pairwise judgments inconsistency and the degree of possible estimation errors for established vector of priority ratios. This research paper overcomes limitations of other examinations which distinguishes it from other papers and emphasizes its novelty.en
dc.formattext
dc.identifier.doi10.15240/tul/001/2019-4-013
dc.identifier.eissn2336-5604
dc.identifier.issn1212-3609
dc.identifier.urihttps://dspace.tul.cz/handle/15240/154272
dc.language.isoen
dc.publisherTechnická Univerzita v Libercics
dc.publisherTechnical university of Liberec, Czech Republicen
dc.publisher.abbreviationTUL
dc.relation.isbasedonAbdelmaguid, T. F., & Elrashidy, W. (2016). Halting decisions for gas pipeline construction projects using AHP: a case study. Operational Research, 19(1), 1–21. https://doi.org/10.1007/s12351-016-0277-2.
dc.relation.isbasedonAczél, J., & Saaty, T. L. (1983). Procedures for synthesizing ratio judgments. Journal of Mathematical Psychology, 27(1), 93–102. https://doi.org/10.1016/0022-2496(83)90028-7.
dc.relation.isbasedonAguarón, J., & Moreno-Jimenez, J. M. (2003). The geometric consistency index: Approximated thresholds. European Journal of Operational Research, 147(1), 137–145. http://dx.doi.org/10.1016/S0377-2217(02)00255-2.
dc.relation.isbasedonAltuzarra, A., Moreno-Jiménez, J. M., & Salvador, M. (2010). Consensus building in AHP-group decision making: a Bayesian approach. Operations Research, 58(6), 1755–1773.
dc.relation.isbasedonAguarón, 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, 245(1-2), 1–15. http://dx.doi.org/10.1007/s10479-014-1576-8.
dc.relation.isbasedonBana 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(3), 1422-1428. http://dx.doi.org/10.1016/j.ejor.2006.09.022.
dc.relation.isbasedonBarzilai, J. (2005). Measurement and preference function modeling. International Transactions in Operational Research, 12(2), 173–183. http://doi.org/10.1111/j.1475-3995.2005.00496.x.
dc.relation.isbasedonBelton, V., & Gear, T. (1983). On a short-coming of Saaty’s method of analytic hierarchies. Omega, 11(3), 228–230.
dc.relation.isbasedonBozóki, S., & Rapcsák, T. (2008). On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. Journal of Global Optimization, 42(2), 157–175. https://doi.org/10.1007/s10898-007-9236-z.
dc.relation.isbasedonBrunelli, M. (2018). A survey of inconsistency indices for pairwise comparisons. International Journal of General Systems, 47(8), 751–771. https://doi.org/10.1080/03081079.2018.1523156.
dc.relation.isbasedonBudescu, D. V., Zwick, R., & Rapoport, A. (1986). A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling. Applied Psychological Measurement, 10(1), 69–78.
dc.relation.isbasedonCondorcet, M. J. A., de (1785). Essai sur l'application de l'analyse ? la probabilité des décisions rendues ? la pluralité des voix. Paris: De l'Imprimerie Royale [facsimile edition New York, NY: Chelsea, 1972].
dc.relation.isbasedonCrawford, G., & Williams, C. (1980). Analysis of subjective judgment matrices. Santa Monica, CA: Rand Corporation R-2572-AF.
dc.relation.isbasedonCrawford, G., & Williams, C. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29(4), 387–405.
dc.relation.isbasedonDijkstra, T. K. (2013). On the extraction of weights from pairwise comparison matrices. Central European Journal of Operations Research, 21(1), 103–123. http://dx.doi.org/10.1007/s10100-011-0212-9.
dc.relation.isbasedonDixit, P. D. (2018). Entropy production rate as a criterion for inconsistency in decision theory. Journal of Statistical Mechanics: Theory and Experiment, (5), 353–408.
dc.relation.isbasedonDong, 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(1), 229–242. https://doi.org/10.1016/j.ejor.2007.01.044.
dc.relation.isbasedonEscobar, M. T., Aguarón, J., & Moreno-Jiménez, J. M. (2004). A note on AHP group consistency for the row geometric mean prioritization procedure. European Journal of Operational Research, 153(2), 318–322. http://doi.org/10.1016/S0377-2217(03)00154-1.
dc.relation.isbasedonFedrizzi, M., & Ferrari, F. (2017). A chi-square-based inconsistency index for pairwise comparison matrices. Journal of the Operational Research Society, 69(7), 1125–1134. https://doi.org/10.1080/01605682.2017.1390523.
dc.relation.isbasedonGrošelj, P., & Stirn, L. Z. (2012). Acceptable consistency of aggregated comparison matrices in Analytic Hierarchy Process. European Journal of Operational Research, 223(2), 417–420. https://doi.org/10.1016/j.ejor.2012.06.016.
dc.relation.isbasedonGrzybowski, A. Z. (2016). New results on inconsistency indices and their relationship with the quality of priority vector estimation. Expert Systems with Applications, 43, 197–212. http://dx.doi.org/10.1016/j.eswa.2015.08.049.
dc.relation.isbasedonGrzybowski, 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. http://dx.doi.org/10.1016/j.eswa.2012.04.051.
dc.relation.isbasedonHosseinian, S. S., Navidi, H., & Hajfathaliha, A. (2012). A new linear programming method for weights generation and group decision making in the Analytic Hierarchy Process. Group Decision and Negotiation, 21(3), 233–254. https://doi.org/10.1007/s10726-009-9182-x.
dc.relation.isbasedonJohnson, C. R., Beine, W. B., & Wang, T. J. (1979). Right-left asymmetry in an eigenvector ranking procedure. Journal of Mathematical Psychology, 19(1), 61–64.
dc.relation.isbasedonKazibudzki, P. T. (2016b). An examination of performance relations among selected consistency measures for simulated pairwise judgments. Annals of Operations Research, 244(2), 525–544. http://dx.doi.org/10.1007/s10479-016-2131-6.
dc.relation.isbasedonKazibudzki, P. T. (2019a). An examination of ranking quality for simulated pairwise judgments in relation to performance of the selected consistency measure. Advances in Operations Research, 2019, 1–24. https://doi.org/10.1155/2019/3574263.
dc.relation.isbasedonKazibudzki, P. T. (2019b). The quality of ranking during simulated pairwise judgments for examined approximation procedures. Modelling and Simulation in Engineering, 2019, 1–13. https://doi.org/10.1155/2019/1683143.
dc.relation.isbasedonKoczkodaj, W. W., & Urban, R. (2018). Axiomatization of inconsistency indicators for pairwise comparisons. International Journal of Approximate Reasoning, 94, 18–29. https://doi.org/10.1016/j.ijar.2017.12.001.
dc.relation.isbasedonKoczkodaj, W. W., & Szwarc, R. (2014). On axiomatization of inconsistency indicators for pairwise comparisons. Fundamenta Informaticae, 132(4), 485–500. http://doi.org/10.3233/FI-2014-1055.
dc.relation.isbasedonKou, G., Ergu, D., Lin, C., & Chen, Y. (2016). Pairwise comparison matrix in multiple criteria decision making. Technological and Economic Development of Economy, 22(5), 738–765. http://doi.org/10.3846/20294913.2016.1210694.
dc.relation.isbasedonKramulová, J., & Jablonský, J. (2016). AHP model for competitiveness analysis of selected countries. Central European Journal of Operations Research, 24(2), 335–351. https://doi.org/10.1007/s10100-015-0394-7.
dc.relation.isbasedonKułakowski, K. (2015). A heuristic rating estimation algorithm for the pairwise comparisons method. Central European Journal of Operations Research, 23(1), 187–203. https://doi.org/10.1007/s10100-013-0311-x.
dc.relation.isbasedonLidinska, L., & Jablonsky, J. (2018). AHP model for performance evaluation of employees in a Czech management consulting company. Central European Journal of Operations Research, 26(1), 239–258. https://doi.org/10.1007/s10100-017-0486-7.
dc.relation.isbasedonLinares, P. (2009). Are Inconsistent Decisions Better? An Experiment with Pairwise Comparisons, European Journal of Operational Research, 193(2), 492–498.
dc.relation.isbasedonLinares, P., Lumbreras, S., Santamaría, A., & Veiga, A. (2016). How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP. Annals of Operations Research, 245(1-2), 227–244. https://doi.org/10.1007/s10479-014-1767-3.
dc.relation.isbasedonLiu, F., Zhang, W.-G., & Wang, Z.-X. (2012). A goal programming model for incomplete interval multiplicative preference relations and its application in group decision making. European Journal of Operational Research, 218(3), 747–754. https://doi.org/10.1016/j.ejor.2011.11.042
dc.relation.isbasedonMerkin, B. G. (1979). Group choice. New York, NY: John Wiley & Sons.
dc.relation.isbasedonMizuno, T. (2019). A link diagram for pairwise comparisons. In: Czarnowski I, Howlett RJ, Jain LC, and Vlacic L. (ed) (2018) Intelligent Decision Technologies. 181–186. Berlin: Springer International Publishing.
dc.relation.isbasedonMoreno-Jiménez, J. M., Aguarón, J., & Escobar, M. T. (2008). The core of consistency in AHP-group decision making. Group Decision and Negotiation, 17(3), 249–265. https://doi.org/10.1007/s10726-007-9072-z.
dc.relation.isbasedonMoreno-Jimenez, J. M., Joven, J. A., Pirla, A. R., & Lanuza, A. T. (2005). A spreadsheet module for consistent consensus building in AHP-group decision making. Group Decision and Negotiation, 14(2), 89–108. https://doi.org/10.1007/s10726-005-2407-8.
dc.relation.isbasedonOrbán-Mihálykó, É., Mihálykó, C., & Koltay, L. (2017). A generalization of the Thurstone method for multiple choice and incomplete paired comparisons. Central European Journal of Operations Research, 27(1), 133–159. https://doi.org/10.1007/s10100-017-0495-6.
dc.relation.isbasedonPeláez, J. I., Martínez, E. A., & Vargas, L. G. (2018). Consistency in positive reciprocal matrices: an improvement in measurement methods. IEEE access 6: 25600–25609.
dc.relation.isbasedonPonis, S. T., Gayialis, S. P., Tatsiopoulos, I. P., Panayiotou, N. A., Stamatiou, D.-R. I., & Ntalla, A. C. (2015). An application of AHP in the development process of a supply chain reference model focusing on demand variability. Operational Research, 15(3), 337–357. https://doi.org/10.1007/s12351-014-0163-8.
dc.relation.isbasedonSaaty, T. L. (1980). The Analytic Hierarchy Process. New York, NY: McGraw Hill.
dc.relation.isbasedonSaaty, T. L. (2006). Fundamentals of decision making and priority theory with the Analytic Hierarchy Process. Pittsburgh, PA: RWS Publication.
dc.relation.isbasedonSaaty, T. L. (2008a). Decision making with the Analytic Hierarchy Process. International Journal of Services Sciences, 1(1), 83–98. https://doi.org/10.1504/IJSSCI.2008.017590.
dc.relation.isbasedonSaaty, T. L. (2008b). Relative measurement and its generalization in decision making. Why pairwise comparisons are central in mathematics for the measurement of intangible factors. The Analytic Hierarchy/Network Process. Revista de la Real Academia de Ciencias Exactas, Fi?sicas y Naturales. Serie A, Matema?ticas, 102(2), 251–318. https://doi.org/10.1007/BF03191825.
dc.relation.isbasedonSaaty, T. L., & Peniwati, K. (2008). Group decision making. Pittsburgh, PA: RWS Publications.
dc.relation.isbasedonSaaty, T. L., & Vargas, L. G. (1984). Comparison of eigenvalue, logarithmic least square and least square methods in estimating ratio. Mathematical Modeling, 5(5), 309–324. https://doi.org/10.1016/0270-0255(84)90008-3.
dc.relation.isbasedonSaaty, T. L., & Vargas, L. G. (2012). The possibility of group choice: pairwise comparisons and merging functions. Social Choice and Welfare, 38(3), 481–496.
dc.relation.isbasedonScala, N. M., Rajgopal, J., Vargas, L. G., & Needy, K. L. (2016). Group decision making with dispersion in the Analytic Hierarchy Process. Group Decision and Negotiation, 25(2), 355–372. https://doi.org/10.1007/s10726-015-9445-7.
dc.relation.isbasedonSchoner, B., & Wedley, W. C. (1989). Ambiguous criteria weights in AHP: Consequences and solutions. Decision Sciences, 20(3), 462–475. https://doi.org/10.1111/j.1540-5915.1989.tb01561.x.
dc.relation.isbasedonSun, L., & Greenberg, B. S. (2006). Multicriteria Group Decision Making: Optimal Priority Synthesis from Pairwise Comparisons. Journal of Optimization Theory and Applications, 130(2), 317–338.
dc.relation.isbasedonTemesi, J. (2011). Pairwise comparison matrices and the error-free property of the decision maker. Central European Journal of Operations Research, 19(2), 239–249. https://doi.org/10.1007/s10100-010-0145-8.
dc.relation.isbasedonThurstone, L. L. (1927). A law of comparative judgments. Psychological Reviews, 34, 273–286.
dc.relation.isbasedonWu, W., & Kou, G. (2016). A group consensus model for evaluating real estate investments alternatives. Financial Innovation, 2(8), 1–10. https://doi.org/10.1186/s40854-016-0027-8.
dc.relation.isbasedonXu, W. J., Dong, Y. C., & Xiao, W. L. (2008). Is it reasonable for Saaty’s consistency test in the pairwise comparison method? Proceedings of 2008 ISECS International Colloquium on Computing, Communication, Control, and Management, 3, 294–298.
dc.relation.isbasedonXu, Z. S. (2000). On consistency of weighted geometric mean complex judgment matrix in AHP. European Journal of Operations Research, 126(3), 683–687. https://doi.org/10.1016/S0377-2217(99)00082-X.
dc.relation.isbasedonYoung, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82(4), 1231–1244. https://doi.org/10.2307/1961757.
dc.relation.isbasedonZahedi, F. (1986). A simulation study of estimation methods in the analytic hierarchy process. Socio-Economic Planning Science, 20(6), 347–354. https://doi.org/10.1016/0038-0121(86)90046-7.
dc.relation.ispartofEkonomie a Managementcs
dc.relation.ispartofEconomics and Managementen
dc.relation.isrefereedtrue
dc.rightsCC BY-NC
dc.subjectgroup decision makingen
dc.subjectAHPen
dc.subjectprioritization qualityen
dc.subjectpairwise judgments consistencyen
dc.subject.classificationD70
dc.subject.classificationC02
dc.subject.classificationC15
dc.subject.classificationC44
dc.subject.classificationC63
dc.titlePairwise judgments consistency impact on quality of multi-criteria group decision-making with AHP[S1]en
dc.typeArticleen
local.accessopen
local.citation.epage212
local.citation.spage195
local.facultyFaculty of Economics
local.filenameEM_4_2019_13
local.fulltextyes
local.relation.abbreviationE+Mcs
local.relation.abbreviationE&Men
local.relation.issue4
local.relation.volume22
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
EM_4_2019_13.pdf
Size:
1.34 MB
Format:
Adobe Portable Document Format
Description:
článek
Collections