Production
https://prod.org.br/article/doi/10.1590/0103-6513.20210045
Production
Thematic Section - Advances in Analytic Hierarchy Process

An update on combinatorial method for aggregation of expert judgments in AHP

Sergii Kadenko; Vitaliy Tsyganok; Zsombor Szádoczki; Sándor Bozóki

Downloads: 0
Views: 30

Abstract

Paper aims: the paper aims to demonstrate the advantages of several modifications of combinatorial method of expert judgment aggregation in AHP. Modifications are based on 1) weighting of spanning trees; 2) sorting of spanning trees by graph diameter during aggregation.

Originality: Both the method and its modifications are developed and improved by the authors. We propose to 1) weight spanning trees, based on quality of respective expert estimates, and 2) sort them by diameter in order to reduce the impact of expert errors and the method’s computational complexity.

Research method: we focus on theoretical and empirical studies of several modifications of combinatorial method of aggregation of expert judgments within AHP.

Main findings: modified combinatorial method has several conceptual advantages over ordinary method. It is also less sensitive to perturbations of initial data. Additionally, selection of spanning trees with smaller diameters allows us to reduce computational complexity of the method and minimize the impact of expert errors.

Implications for theory and practice: Combinatorial method is a universal instrument of expert judgment aggregation, applicable to additive/multiplicative, complete/incomplete, individual/group pair-wise comparisons, provided in different scales. It is used in the original strategic planning technology, which has recently found several important applications.

Keywords

Pair-wise comparison. Consistency. Compatibility. Spanning tree graph diameter. Prüfer sequence.

References

Bozóki, S., & Tsyganok, V. (2019). The (logarithmic) least squares optimality of the arithmetic (geo-metric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices. International Journal of General Systems, 48(4), 362-381. http://dx.doi.org/10.1080/03081079.2019.1585432.

Brunelli, M., & Fedrizzi, M. (2011). Characterizing properties for inconsistency indices in AHP. In Proceedings of the XI International Symposium for the Analytic Hierarchy Process (ISAHP-2011). Retrieved in 2021, May 25, from http://www.isahp.org/uploads/55_064_fedrizzi.pdf

Cayley, A. (1889). A theorem on trees. The Quarterly Journal of Mathematics, 23, 376-378.

Choo, E. U., & Wedley, W. C. (2004). A common framework for deriving priority vectors from pairwise comparison matrices. Computers & Operations Research, 31(6), 893-908. http://dx.doi.org/10.1016/S0305-0548(03)00042-X.

Ferrari Neto, G., Lapasini Leal, G. C., Cardoza Galdamez, E. V., & de Souza, R. C. T. (2020). Prioritization of occupational health and safety indicators using the Fuzzy-AHP method. Production, 30, e20200054. http://dx.doi.org/10.1590/0103-6513.20200054.

Forman, E., & Peniwati, K. (1998). Aggregating individual judgments and priorities with the analytic hierarchy process. European Journal of Operational Research, 108(1), 131-145. http://dx.doi.org/10.1016/S0377-2217(97)00244-0.

Hartley, R. (1928). Transmission of information. The Bell System Technical Journal, 7(3), 535-563. http://dx.doi.org/10.1002/j.1538-7305.1928.tb01236.x.

Holland, J. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.

Iida, Y. (2009). Ordinality consistency test about items and notation of a pairwise comparison matrix in AHP. In Proceedings of the X International Symposium for the Analytic Hierarchy Process (ISAHP-2009). Pittsburgh: AHP. Retrieved in 2021, May 25, from http://isahp.org/2009Proceedings/Final_Papers/32_Iida_Youichi_ConsistencyTest_in_Japan_REV_FIN.pdf

Kadenko, S., & Tsyganok, V. (2020). An update on combinatorial method for aggregation of expert judgments in AHP. In Proceedings of the International Symposium on the Analytic Hierarchy Process (ISAHP-2020). Pittsburgh: AHP. Retrieved in 2021, May 25, from http://www.isahp.org/uploads/035.pdf

Kułakowski, K. (2020). On the geometric mean method for incomplete pairwise comparisons. Mathematics, 8(11), 1873. http://dx.doi.org/10.3390/math8111873.

Lipovetsky, S. (2021). AHP in nonlinear scaling: from two-envelope problem to modeling by predictors. Production, 31, e20210007. http://dx.doi.org/10.1590/0103-6513.20210007.

Lundy, M., Siraj, S., & Greco, S. (2017). The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis. European Journal of Operational Research, 257(1), 197-208. http://dx.doi.org/10.1016/j.ejor.2016.07.042.

Mikhailov, L., & Siraj, S. (2011). Improving the ordinal consistency of pairwise comparison matrices. In Proceedings of the XI International Symposium for the Analytic Hierarchy Process (ISAHP-2011). Pittsburgh: AHP. http://dx.doi.org/10.13033/isahp.y2011.128.

Olenko, A., & Tsyganok, V. (2016). Double entropy inter-rater agreement indices. Applied Psychological Measurement, 40(1), 37-55. http://dx.doi.org/10.1177/0146621615592718. PMid:29881035.

Oliveira Ramos, M., Silva, E. M., & Lima-Júnior, F. R. (2020). A fuzzy AHP approach to select suppliers in the Brazilian food supply chain. Production, 30, e20200013. http://dx.doi.org/10.1590/0103-6513.20200013.

Prüfer, H. (1918). Neuer Beweis eines Satzes über Permutationen. Archiv der Mathematik und Physik, 27, 742-744.

Saaty, T. (1980). The analytic hierarchy process. New York: McGraw-Hill.

Saaty, T. (1996). Decision making with dependence and feedback: the analytic network process. Pittsburgh: RWS Publicaitons.

Saaty, T. L., & Peniwati, K. (2007). Group decision-making: drawing out and reconciling differences. Pittsburgh: RWS Publications.

Siraj, S., Mikhailov, L., & Keane, J. (2012). Enumerating all spanning trees for pairwise comparisons. Computers & Operations Research, 39(2), 191-199. http://dx.doi.org/10.1016/j.cor.2011.03.010.

Szádoczki, Zs., Bozóki, S., & Tekile, A. H. (2020). Proposals for the set of pairwise comparisons. In Proceedings of the International Symposium on the Analytic Hierarchy Process (ISAHP-2020). Pittsburgh: AHP. Retrieved in 2021, May 25, from http://www.isahp.org/uploads/057_001.pdf

Totsenko, V. G. (1996). The agreement degree of estimations set with regard for experts’ competence. In Proceedings of the IV International Symposium on the AHP (ISAHP ’96) (pp. 229-241). Burnaby: Simon Fraser University.

Tsyganok, V. (2000). Combinatorial method of pair-wise comparisons with feedback (in Ukrainian). Data Recording. Baoxian Yu Jiagong, 2, 92-102.

Tsyganok, V. (2010). Investigation of the aggregation effectiveness of expert estimates obtained by the pairwise comparison method. Mathematical and Computer Modelling, 52(3-4), 538-544. http://dx.doi.org/10.1016/j.mcm.2010.03.052.

Tsyganok, V. V., Kadenko, S. V., & Andriichuk, O. V. (2011). Simulation of expert judgements for testing the methods of information processing in decision-making support systems. Journal of Automation and Information Sciences, 43(12), 21-32. http://dx.doi.org/10.1615/JAutomatInfScien.v43.i12.30.

Tsyganok, V. V., Kadenko, S. V., & Andriichuk, O. V. (2015). Using different pair-wise comparison scales for developing industrial strategies. International Journal of Management and Decision Making, 14(3), 224-250. http://dx.doi.org/10.1504/IJMDM.2015.070760.

Tsyganok, V., Kadenko, S., & Andriychuk, O. (2020). Hybrid decision support methodology based on objective and expert data. In 2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT) (pp. 265-271). New York: IEEE. http://dx.doi.org/10.1109/DESSERT50317.2020.9125022.

Tsyganok, V., Kadenko, S., Andriichuk, O., & Roik, P. (2018). Combinatorial method for aggregation of incomplete group judgments. In Proceedings of 2018 IEEE 1st International Conference on System Analysis & Intelligent Computing (SAIC) (pp. 25-30). New York: IEEE. http://dx.doi.org/10.1109/SAIC.2018.8516768.

Tsyganok, V., Kadenko, S., Andriychuk, O., & Roik, P. (2017). Usage of multicriteria decision‐making support arsenal for strategic planning in environmental protection sphere. Journal of Multi-criteria Decision Analysis., 24(5-6), 227-238. http://dx.doi.org/10.1002/mcda.1616.

Wollmann, D., Steiner, M. T. A., Vieira, G. E., & Steiner, P. A. (2014). Details of the analytic hierarchy process technique for the evaluation of health insurance companies. Production, 24(3), 583-593. http://dx.doi.org/10.1590/S0103-65132013005000070.

Wu, B. Y., & Chao, K.-M. (2004). Spanning trees and optimization problems. USA: Chapman & Hall/CRC Press. http://dx.doi.org/10.1201/9780203497289.
 


Submitted date:
05/27/2021

Accepted date:
08/25/2021

614e14bda953952f82128232 production Articles
Links & Downloads

Production

Share this page
Page Sections