To solve multi-criteria problems, several methods of decision-making are increasingly applied at the same time. It allows to find more precise solution to a problem on many criteria. In this case, a pressing need to ensure consistency between decisions obtained via different methods arises. In the current research, much attention has been attached to the consistency assessment employing different rank correlation coefficients. However, little attention has been given to application of metrics, reflecting general consistency for three and more rank sequences; and emphasis has been placed on conducting pairwise assessment of multi-criteria decision-making methods with one another. The paper is devoted to answering the question of whether the consistency between pairs of multi-criteria decision-making methods can reflect the consistency within the group of these methods. An experiment was conducted on the example of a problem of determining the rating of university departments with the use of three methods of multi-criteria decision-making and two metrics of rank correlation: Kendall's coefficient of concordance and Kendall’s rank correlation coefficient. The experiment results show that for the test case all the three methods give an agreed outcome, while the rankings of each pair of methods are inconsistent.
1. Pagone E., Salonitis K. Comparative Study of Multi-Criteria Decision Analysis Methods in Environmental Sustainability. In: Sustainable Design and Manufacturing: Proceedings of the 9th International Conference on Sustainable Design and Manufacturing (SDM 2022), 14–16 September 2022, Split, Croatia. Singapore: Springer; 2023. P. 223–231. https://doi.org/10.1007/978-981-19-9205-6_21
2. Latypova V.A. Multi Criteria Decision-Making with the Use of ELECTRE Methods Group. Modeling, Optimization and Information Technology. 2024;12(4). (In Russ.). https://doi.org/10.26102/2310-6018/2024.47.4.030
3. Mukhametzyanov I.Z. Normalization and MCDM Rank Model. In: Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems: Inversion, Displacement, Asymmetry. Cham: Springer; 2023. P. 41–69. https://doi.org/10.1007/978-3-031-33837-3_3
4. Aydin F., Gümüs B. Comparative Analysis of Multi-Criteria Decision Making Methods for the Assessment of Optimal SVC Location. Bulletin of the Polish Academy of Sciences. Technical Sciences. 2022;70(2). https://doi.org/10.24425/bpasts.2022.140555
5. Kabassi K., Bekatoros S., Botonis A. Checking Consistency and Comparing Multi-Criteria Decision Making Methods in the Evaluation of Museums' Websites. Digital. 2022;2(4):484–500. https://doi.org/10.3390/digital2040026
6. Shekhovtsov A., Sałabun W. A Comparative Case Study of the VIKOR and TOPSIS Rankings Similarity. Procedia Computer Science. 2020;176:3730–3740. https://doi.org/10.1016/j.procs.2020.09.014
7. Sałabun W., Urbaniak K. A New Coefficient of Rankings Similarity in Decision-Making Problems. In: Computational Science – ICCS 2020: 20th International Conference: Proceedings: Part II, 03–05 June 2020, Amsterdam, The Netherlands. Cham: Springer; 2020. P. 632–645. https://doi.org/10.1007/978-3-030-50417-5_47
8. Mian S.H., Nasr E.A., Moiduddin Kh., Saleh M., Abidi M.H., Alkhalefah H. Assessment of Consolidative Multi-Criteria Decision Making (C-MCDM) Algorithms for Optimal Mapping of Polymer Materials in Additive Manufacturing: A Case Study of Orthotic Application. Heliyon. 2024;10(10). https://doi.org/10.1016/j.heliyon.2024.e30867
9. Rajabi F., Molaeifar H., Jahangiri M., Taheri Sh., Banaee S., Farhadi P. Occupational Stressors Among Firefighters: Application of Multi-Criteria Decision Making (MCDM) Techniques. Heliyon. 2020;6(4). https://doi.org/10.1016/j.heliyon.2020.e03820
10. Latypova V.A. Support for Decision-Making in Assigning Code Reviewers. In: Intelligent Systems: 16th International Conference on Intelligent Systems, INTELS 2024: Proceedings: Part II, 02–04 December 2024, Moscow, Russia. Cham: Springer; 2025. P. 182–194. https://doi.org/10.1007/978-3-032-04761-8_14
11. Latypova V.A. Decision Support Methods for Managing the Solution of Complex Open Problems Based on Intelligent Analysis of Error Messages. Systems Engineering and Information Technologies. 2023;5(5):52–67. (In Russ.).
12. Kou G., Lu Y., Peng Y., Shi Y. Evaluation of Classification Algorithms Using MCDM and Rank Correlation. International Journal of Information Technology & Decision Making. 2012;11(1):197–225. https://doi.org/10.1142/S0219622012500095
13. Kizielewicz B., Shekhovtsov A., Sałabun W. A New Approach to Eliminate Rank Reversal in the MCDA Problems. In: Computational Science – ICCS 2021: 21st International Conference: Proceedings: Part I, 16–18 June 2021, Krakow, Poland. Cham: Springer; 2021. P. 338–351. https://doi.org/10.1007/978-3-030-77961-0_29
14. Saaty T.L. On the Measurement of Intangibles. A Principal Eigenvector Approach to Relative Measurement Derived from Paired Comparisons. Cloud of Science. 2015;2(1):5–39. (In Russ.).
15. Latypova V.A. A Choice of the Optimal Method for Implementation of Training Control Tool Using Analytic Hierarchy Process. Engineering Journal of Don. 2017;(2). (In Russ.). URL: http://www.ivdon.ru/en/magazine/archive/N2y2017/4120
16. Shekhovtsov A. How Strongly Do Rank Similarity Coefficients Differ Used in Decision Making Problems? Procedia Computer Science. 2021;192:4570–4577. https://doi.org/10.1016/j.procs.2021.09.235
17. Kendall M.G. Rank Correlation Methods. Griffin; 1970. 202 p.
18. Pohl E., Geldermann J. PROMETHEE-Cloud: A Web App to Support Multi-Criteria Decisions. EURO Journal on Decision Processes. 2024;12. https://doi.org/10.1016/j.ejdp.2024.100053
19. Vorob'ev A.E., Murzaeva A.K. Technique of the Efficiency Assessment of Activity of in Higher Educational Department Institution. Vestnik Donetskogo pedagogicheskogo instituta. 2017;(4):135–146. (In Russ.).
