A Novel Approach to Weighting Criteria Based on Rank Stability

Abstract

In Multi-Criteria Decision Making (MCDM), the weighting of the criteria is at least as important as the normalization of the decision matrix and the procedure for ranking the alternatives. The slightest uncertainty in the weights of criteria poses a major problem for decision-makers, especially when there is little difference between the assessments of alternatives. One crucial question is which approaches should be applied to a given MCDM problem? This question may be answered by considering the insensitivity of rankings of the alternatives to changes in the weights of criteria. We propose a novel approach to criteria weighting that focuses solely on the insensitivity of rankings to changes in the weights of criteria. Simulations reveal that this approach is superior to other existing methods in terms of ranking stability. A real-life example concerning the digital readiness of the European Union reveals that this new approach yields beneficial results in different aspects of decision-making.

Keywords

• decision-making
• objective weighting
• MCDM
• rank stability
• digital readiness.

Sıralama İstikrarına Dayalı Kriterlerin Ağırlıklandırılmasına Yönelik Yeni Bir Yaklaşım

Abstract

Çok Kriterli Karar Verme'de (ÇKKV), kriterlerin ağırlıklandırılması, karar matrisinin normalizasyonu ve alternatifleri sıralama prosedürü kadar önemlidir. Kriter ağırlıklarındaki en ufak belirsizlik, özellikle alternatiflerin değerlendirmeleri arasında çok az fark olduğunda, karar vericiler için büyük bir sorun teşkil eder. Önemli sorulardan biri, belirli bir ÇKKV problemine hangi yaklaşımların uygulanması gerektiğidir? Bu soru, alternatiflerin sıralamalarının kriter ağırlıklarındaki değişikliklere duyarsızlığı dikkate alınarak cevaplanabilir. Kriter ağırlıklandırmasına, yalnızca sıralamaların kriter ağırlıklarındaki değişikliklere duyarsızlığına odaklanan yeni bir yaklaşım öneriyoruz. Simülasyonlar, bu yaklaşımın sıralama istikrarı açısından diğer mevcut yöntemlerden üstün olduğunu ortaya koymaktadır. Avrupa Birliği'nin dijital hazırbulunuşluğuna ilişkin gerçek hayattan bir örnek, bu yeni yaklaşımın karar vermenin farklı yönlerinde faydalı sonuçlar verdiğini ortaya koymaktadır.

Keywords

• karar alma
• nesnel ağırlıklandırma
• sıralama istikrarı
• dijital hazırlık.
• ÇKKV

References

1. Akdag, H., Kalaycı, T., Karagöz, S., Zülfikar, H., & Giz, D. (2014). The evaluation of hospital service quality by fuzzy MCDM. Applied Soft Computing, 23, 239-248. Doi: https://doi.org/10.1016/j.asoc.2014.06.033
2. Alptekin, G. I., & Büyüközkan, G. (2011). An integrated case-based reasoning and MCDM system for Web based tourism destination planning. Expert Systems with Applications, 38(3), 2125-2132. Doi: https://doi.org/10.1016/j.eswa.2010.07.153
3. Anojkumar, L., Ilangkumaran, M., & Sasirekha, V. (2014). Comparative analysis of MCDM methods for pipe material selection in sugar industry. Expert systems with applications, 41(6), 2964-2980. Doi: https://doi.org/10.1016/j.eswa.2013.10.028
4. Baydaş, M., & Elma, O. E. (2021). An objectıve criteria proposal for the comparison of MCDM and weighting methods in financial performance measurement: An application in Borsa Istanbul. Decision Making: Applications in Management and Engineering, 4(2), 257-279. Doi: https://doi.org/10.31181/dmame210402257b
5. Büyüközkan, G., & Güler, M. (2021). A combined hesitant fuzzy MCDM approach for supply chain analytics tool evaluation. Applied Soft Computing, 112, 107812. Doi: https://doi.org/10.1016/j.asoc.2021.107812
6. Chatterjee, P., Mondal, S., Boral, S., Banerjee, A., & Chakraborty, S. (2017). A novel hybrid method for non-traditional machining process selection using factor relationship and Multi-Attributive Border Approximation Method. Facta Universitatis, Series: Mechanical Engineering, 15(3), 439-456. Erişim Linki: https://casopisi.junis.ni.ac.rs/index.php/FUMechEng/article/view/2839/1968
7. Chen, Y. C., Lien, H. P., & Tzeng, G. H. (2010). Measures and evaluation for environment watershed plans using a novel hybrid MCDM model. Expert systems with applications, 37(2), 926-938. Doi: https://doi.org/10.1016/j.eswa.2009.04.068
8. Chen, Y. S., Chuang, H. M., Sangaiah, A. K., Lin, C. K., & Huang, W. B. (2019). A study for project risk management using an advanced MCDM-based DEMATEL-ANP approach. Journal of Ambient Intelligence and Humanized Computing, 10, 2669-2681. Erişim Linki: https://link.springer.com/article/10.1007/s12652-018-0973-2

9. CISCO Digital Readiness Index. Retrieved from https://www.cisco.com/c/m/en_us/about/corporate-social-responsibility/research-resources/digital-readiness-index.html#/ . Accessed 05 January 2023. Çarman, F., & Tuncer Şakar, C. (2019). An MCDM-integrated maximum coverage approach for positioning of military surveillance systems. Journal of the Operational Research Society, 70(1), 162-176. Doi: https://doi.org/10.1080/01605682.2018.1442651
10. Danielson, M., & Ekenberg, L. (2017). A robustness study of state-of-the-art surrogate weights for MCDM. Group Decision and Negotiation, 26(4), 677-691. Erişim Linki: https://link.springer.com/article/10.1007/s10726-016-9494-6 Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763-770. Doi: https://doi.org/10.1016/0305-0548(94)00059-H
11. Ecer, F., & Pamucar, D. (2022). A novel LOPCOW-DOBI multi-criteria sustainability performance assessment methodology: An application in developing country banking sector. Omega, 102690. Doi: https://doi.org/10.1016/j.omega.2022.102690 Eisenhardt, K. M., & Zbaracki, M. J. (1992). Strategic decision making. Strategic management journal, 13(S2), 17-37. Doi: https://doi.org/10.1002/smj.4250130904 Esangbedo,
12. M. O., Bai, S., Mirjalili, S., & Wang, Z. (2021). Evaluation of human resource information systems using grey ordinal pairwise comparison MCDM methods. Expert Systems with Applications, 182, 115151. Doi: https://doi.org/10.1016/j.eswa.2021.115151
13. Hwang, C.L. & Yoon, K. Multiple Attribute Decision-making: Methods and Applications, Springer, Berlin, 1981. Erişim Linki: https://link.springer.com/chapter/10.1007/978-3-642-48318-9_3
14. Jessop, A. (2004). Sensitivity and robustness in selection problems. Computers & Operations Research, 31(4), 607-622. Doi: https://doi.org/10.1016/S0305-0548(03)00017-0 Karsak, E. E., & Dursun, M. (2015). An integrated fuzzy MCDM approach for supplier evaluation and selection. Computers & Industrial Engineering, 82, 82-93.
15. Doi: https://doi.org/10.1016/j.cie.2015.01.019 Kazancoglu, Y., & Ozkan-Ozen, Y. D. (2019). Lean in higher education: A proposed model for lean transformation in a business school with MCDM application. Quality Assurance in Education, 27(1), 82-102. Doi: https://doi.org/10.1108/QAE-12-2016-0089 Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2021). Determination of objective weights using a new method based on the removal effects of criteria (MEREC). Symmetry, 13(4), 525.
16. https://doi.org/10.3390/sym13040525 Lee, H. C., & Chang, C. T. (2018). Comparative analysis of MCDM methods for ranking renewable energy sources in Taiwan. Renewable and sustainable energy reviews, 92, 883-896. Doi: https://doi.org/10.1016/j.rser.2018.05.007
17. Lin, Y. T., Lin, C. L., Yu, H. C., & Tzeng, G. H. (2010). A novel hybrid MCDM approach for outsourcing vendor selection: A case study for a semiconductor company in Taiwan. Expert systems with applications, 37(7), 4796-4804. Doi: https://doi.org/10.1016/j.eswa.2009.12.036
18. Liou, J. J., Lu, M. T., Hu, S. K., Cheng, C. H., & Chuang, Y. C. (2017). A hybrid MCDM model for improving the electronic health RRCd to better serve client needs. Sustainability, 9(10), 1819. Doi: https://doi.org/10.3390/su9101819 Mardani,
19. A., Jusoh, A., Nor, K., Khalifah, Z., Zakwan, N., & Valipour, A. (2015). Multiple criteria decision-making techniques and their applications–a review of the literature from 2000 to 2014. Economic research-Ekonomska istraživanja, 28(1), 516-571. Doi: https://doi.org/10.1080/1331677X.2015.1075139
20. Özbekler, T. M., & Akgül, A. K. (2025). A GIS-based Multi-Criteria Decision-Making Approach for Location Selection of Urban Micro-Consolidation Centers Under Sustainability. Journal of Turkish Operations Management, 9(1), 158-180. Doi: https://doi.org/10.56554/jtom.1615906
21. Pala, O. (2022). A mixed-integer linear programming model for aggregating multi–criteria decision making methods. Decision Making: Applications in Management and Engineering, 5(2), 260-286. Doi: https://doi.org/10.31181/dmame0318062022p
22. Pala, O. (2023). A New Objective Weighting Method Based On Robustness of Ranking with Standard Deviation and Correlation: the Rocosd Method. Information Sciences. 636. Doi: https://doi.org/10.1016/j.ins.2023.04.009
23. Pala, O. (2024). Assessment of the social progress on European Union by logarithmic decomposition of criteria importance. Expert Systems with Applications, 238, 121846. Doi: https://doi.org/10.1016/j.eswa.2023.121846
24. Radmehr, A., Bozorg-Haddad, O., & Loáiciga, H. A. (2022). Developing strategies for agricultural water management of large irrigation and drainage networks with Fuzzy MCDM. Water Resources Management, 36(13), 4885-4912. Erişim Linki: https://link.springer.com/article/10.1007/s11269-022-03192-3
25. Soygüder, S., & Geçer, E. (2023). Application of Multi-Criteria Decision-Making Methods in Supplier Selection. Journal of Optimization and Decision Making, 2(2), 349-356. Erişim Linki: https://dergipark.org.tr/en/pub/jodm/issue/81776/1285844
26. Su, J., Xu, B., Liu, H., Chen, Y., & Zhang, X. (2025). A Probabilistic Hesitant Fuzzy Multi-Criteria Decision-Making Method Based on CSOGRMILP and Borda-CoCoSo. International Journal of Fuzzy Systems, 1-18. Doi: https://doi.org/10.1007/s40815-025-01988-0
27. Tzeng, G. H., & Huang, C. Y. (2012). Combined DEMATEL technique with hybrid MCDM methods for creating the aspired intelligent global manufacturing & logistics systems. Annals of Operations Research, 197, 159-190. Doi: https://doi.org/10.1007/s10479-010-0829-4 Uyala,
28. S. B., Uyala, S., Jannu, S., & Gadakh, V. S. (2024). Multi-Objective Optimization Of Machining Parameters For Edm Of Magnesium Alloy-Ze41 Using Marcos Algorithm And Different Weighing Methods: Sd, Critic And Merec. International Journal of Modern Manufacturing Technologies (IJMMT), 16(1). Doi: https://doi.org/ 10.54684/ijmmt.2024.16.1.124
29. Vinogradova-Zinkevič, I. (2024). Centroidous Method for Determining Objective Weights. Mathematics, 12(14), 2269. Doi: https://doi.org/10.3390/math12142269
30. Wang, T. C., & Lee, H. D. (2009). Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert systems with applications, 36(5), 8980-8985. Doi: https://doi.org/10.1016/j.eswa.2008.11.035
31. Wang, Y. M., & Luo, Y. (2010). Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making. Mathematical and Computer Modelling, 51(1-2), 1-12. Doi: https://doi.org/10.1016/j.mcm.2009.07.016
32. Zavadskas, E. K., & Podvezko, V. (2016). Integrated determination of objective criteria weights in MCDM. International Journal of Information Technology & Decision Making, 15(02), 267-283. Doi: https://doi.org/10.1142/S0219622016500036
33. Zeleny, M. (1998). Multiple criteria decision making: Eight concepts of optimality. Human Systems Management, 17(2), 97-107. Doi: https://doi.org/10.3233/HSM-1998-17203
34. Zhang, X., Wang, C., Li, E., & Xu, C. (2014). Assessment model of ecoenvironmental vulnerability based on improved entropy weight method. The Scientific World Journal, 2014. Doi: https://doi.org/10.1155/2014/797814