A Novel Method for Objective Criterion Weighting: The Neyman Chi-Square Distance Approach (NCDA)

Öz

In the context of Multi-Criteria Decision-Making (MCDM), most objective weighting techniques tend to focus either solely on internal variability (e.g., ENTROPY, SD, SVP, LOPCOW) or exclusively on external structural effects (e.g., MEREC). Although the CRITIC method considers both dimensions, it remains constrained by its dependence on linear associations and parametric assumptions—particularly the assumption of normality. Such methodological limitations can undermine the reliability of decision outcomes and constitute the central motivation of this study. To address this limitation, the study introduces an innovative framework termed the Neyman Chi-Square Distance Approach (NCDA). NCDA is a non-parametric method that simultaneously accounts for both internal variation and external structural divergence. Standard deviation captures internal variability, while Neyman Chi-Square Distance (NCD) quantifies external differences without relying on correlation assumptions. Empirical analyses and case studies reveal that NCDA demonstrates strong robustness against perturbations in the weighting process, as validated through sensitivity analysis. Comparative evaluations confirm the method’s high consistency with well-established approaches, while simulation experiments highlight its capacity to produce balanced and stable weight distributions. Overall, NCDA provides an original and methodologically rigorous contribution to the field by directly integrating distributional distance analysis into the weighting process of decision-making models. This dual-perspective framework not only strengthens the theoretical foundations but also enhances the adaptability and reliability of MCDM applications across complex and heterogeneous data environments.

Anahtar Kelimeler

• NCD
• Criteria Weight
• MCDM
• NCDA

Nesnel Kriter Ağırlıklandırması için Yeni Bir Yöntem: Neyman Ki-Kare Uzaklık Yaklaşımı (NCDA)

Öz

Çok kriterli karar verme (MCDM) bağlamında, nesnel ağırlıklandırma tekniklerinin büyük çoğunluğu ya yalnızca içsel değişkenliğe (örneğin ENTROPY, SD, SVP, LOPCOW) ya da bütünüyle dışsal yapısal etkilere (örneğin MEREC) odaklanma eğilimindedir. CRITIC yöntemi her iki boyutu bir araya getirse de, özellikle doğrusal ilişkiler ve parametrik varsayımlar (özellikle normallik varsayımı) konusundaki bağımlılığı nedeniyle kısıtlı kalmaktadır. Bu tür metodolojik sınırlılıklar, karar sonuçlarının güvenilirliğini zayıflatabilmekte ve bu çalışmanın temel motivasyonunu oluşturmaktadır. Bu boşluğu gidermek amacıyla, mevcut araştırma hem içsel varyasyonu hem de dışsal yapısal ayrışmayı aynı anda dikkate alan ve parametrik olmayan bir çerçevede tasarlanan yenilikçi bir yöntem olan Neyman Ki-Kare Uzaklık Yaklaşımı’nı (NCDA) önermektedir. İçsel değişkenlik standart sapma aracılığıyla değerlendirilirken, dışsal dağılımsal farklılıklar korelasyona dayalı varsayımlardan kaçınılarak Neyman Ki-Kare Uzaklık (NCD) metriği üzerinden yakalanmaktadır. Ampirik analizler, NCDA’nın ağırlıklandırma üzerindeki değişimlere karşı yapılan duyarlılık analizinde güçlü bir sağlamlık sergilediğini göstermektedir. Karşılaştırmalı değerlendirmeler yöntemin yaygın kabul gören yaklaşımlarla tutarlılığını teyit ederken, simülasyon deneyleri ise dengeli ve istikrarlı ağırlık dağılımları üretebilme kapasitesini ortaya koymaktadır. Genel olarak NCDA, dağılımsal uzaklık analizini karar modellerinin ağırlıklandırma sürecine doğrudan entegre ederek alana özgün ve metodolojik açıdan sağlam bir katkı sunmaktadır. Bu çift yönlü bakış açısı yalnızca teorik temelleri güçlendirmekle kalmayıp aynı zamanda karmaşık ve heterojen veri ortamlarında MCDM uygulamalarının uyarlanabilirliğini ve güvenilirliğini de artırmaktadır.

Anahtar Kelimeler

• NCD
• Kriter ağırlığı
• ÇKKV
• NCDM

Kaynakça

1. Munier, N., Hontoria, E., & Jiménez-Sáez, F. (2019). Strategic approach in multi-criteria decision making: A practical guide for complex scenarios. Springer Verlag, Heilderberg.
2. Lopez, L. M., Ishizaka, A., & Qin, J. (2023). Multi criteria decision making sorting methods: applications to real world. Academic Press, Cambridge-Massachusetts.
3. Kulkarni, A. J. (2022). Multiple criteria decision making: techniques, analysis and applications. Springer Nature, Singapore.
4. Ayçin, E. (2019). Çok kriterli karar verme. Nobel Akademik Yayıncılık, Ankara.
5. Öztel, A., & Alp, İ. (2020). Çok kriterli karar verme seçiminde yeni bir yaklaşım. Kriter Yayıncılık, İstanbul.
6. Dinçer, S. E. (2019). Çok kriterli karar alma. Gece Akademi, Ankara.
7. Ecer, F., & Pamucar, D. (2020). Sustainable supplier selection: A Novel ıntegrated fuzzy best worst method (f-bwm) and fuzzy cocoso with bonferroni (CoCoSo’B) Multi-Criteria Model. Journal of Cleaner Production, 266, 1-18.
8. Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763-770.

9. Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2021). Determination of ObjectiveWeights Using a New Method Based on the Removal Effects of Criteria (MEREC). Symmetry, 13(525), 1-21. https://doi.org/10.3390/sym13040525
10. Zardari, N. H., Ahmed, K., Shirazi, S. M., & Yusop, Z. B. (2014). Weighting Methods and their Effects on Multi Criteria Decision Making Model Outcomes in Water Resources Management. Springer Nature, Berlin.
11. Kilmen, S. (2020). Eğitim araştırmacıları için spss uygulamalı İstatistik. Anı Yayıncılık, Ankara.
12. Kalaycı, Ş. (2013). SPSS uygulamalı çok değişkenli istatistik teknikleri. Anı Yayın Dağıtım, Ankara.
13. Cressie, N., & Read, T. R. (1984). Multinomial goodness-of-fit tests. Journal of The Royal Statistical Society. Series B (Methodological), 46(3), 440-464.
14. Baş, F. (2021). Çok kriterli karar verme yöntemlerinde kriter ağırlıklarının belirlenmesi. Nobel Bilimsel, Ankara.
15. Ecer, F. (2020). Çok kriterli karar verme. Seçkin Yayıncılık, Ankara.
16. Bircan, H. (2020). Çok kriterli karar verme problemlerinde kriter ağırlıklandırma yöntemleri. Nobel Akademik Yayıncılık, Ankara.
17. Banadkouki, M. R. (2023). Selection of strategies to improve energy efficiency in industry: A hybrid approach using entropy weight method and fuzzy TOPSIS. Energy, 279, 1-15. https://doi.org/10.1016/j.energy.2023.128070
18. Liang, J. (2025). Evaluation of design behavior factors weighting based on ahp-entropy weighting method in artificial ıntelligence persfective, AICI '25: Proceedings of the 2025 International Conference on Artificial Intelligence and Computational Intelligence, 15 July, Browse Publications, Kuala Lumpur, Indonesia, 548-552. https://doi.org/10.1145/3730436.3730526
19. Huang, Z. (2025). Research on the coordinated development of urban digital economy based on the “entropy weight-coupling coordination mode, Taking Beijing-Tianjin-Hebei as an Example. Advances in Economics, Business and Management Research:Proceedings of the 2025 5th International Conference on Enterprise Management and Economic Development (ICEMED 2025), 14 August, Dali, China, 346, 328-338. https://doi.org/10.2991/978-94-6463-811-0_35
20. Yang, M., Wu, J., Wang, Y.-X., Wang, Z.-G., & Lan , S.-H. (2025). An optimally improved entropy weight method integrated with a fuzzy comprehensive evaluation for complex environment systems. Environmental and Ecological Statistics, 32, 645–673. https://doi.org/10.1007/s10651-025-00654-w
21. Odu, G. 0. (2019). Weighting methods for multi-criteria decision making technique. J. Appl. Sci. Environ. Manage, 23(8), 1449-1457.
22. Mukhametzyanov, I. Z. (2021). Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD. Decision Making:Applicationsin Management andEngineering, 4(2), 76-105. https://doi.org/10.31181/dmame210402076i
23. Hezam, I. M., Mishra, A. K., Pamucar, D., Rani, P., & Mishra, A. R. (2024). Standard deviation and rank sum-based MARCOS model under intuitionistic fuzzy information for hospital site selection. Kybernetes, 53(10), 3723-3753. https://doi.org/10.1108/K-01-2023-0136
24. Tayalı, H. A., & Timor, M. (2017). Ranking with Statistical Variance Procedure Based Analytic Hierarchy Process. Acta Infologica, 1(1), 31-38.
25. Nasser, A. A., Mansoor , N. A., Alkhulaidi, A. A., Hankal, M., & Al-olofe, M. (2019). A weighted euclidean distance-statistical variance procedure based approach for ımproving the healthcare decision making system in Yemen. Indian Journal of Science and Technology, 12(3), 1-15. https://doi.org/10.17485/ijst/2019/v12i3/140661
26. Keleş, N. (2023). Uygulamalarla klasik ve güncel karar verme yöntemleri. Ankara, Atlas Akademik Basım Yayın Dağıtım.
27. Dhruva, S., Krishankumar, R., Ravichandran, K. S., Kaklauskas, A., Zavadskas, E. K., & Gupta, P. (2025). Selection of waste treatment methods for food sources: an integrated decision model using q-rung fuzzy data, LOPCOW, and COPRAS techniques. Clean Technologies and Environmental Policy, https://doi.org/10.1007/s10098-025-03160-6
28. Gu, T., Hao, E., Wang, C., Zhu, S., & Wang, Y. (2024). CRITIC-PROMETHEE II-Based Evaluation of Smart Community Services: A Case Study of Shenzhen, China. Journal of the Knowledge Economy, 16, 3286–3320. https://doi.org/10.1007/s13132-024-02114-5
29. Han, L., Wang, Y., Li, S., Li, W., & Chen, X. (2025). Evaluation of water resource carrying capacity and analysis of driving factors in the dadu river basin based on the entropy weight method and crıtıc comprehensive evaluation method. Water, 17, 1-21. https://doi.org/10.3390/w17162360
30. Durmuș, Z. (2025). Assessment of renewable energy performance in turkey using a novel ıntegrated msd-crıtıc-rawec model. Journal of Operational and Strategic Analytics, 3(1), 49-64. https://doi.org/10.56578/josa030105
31. Bakioğlu, G. (2025). Prioritization of digital technology applications in ıntermodal freight transport using crıtıc-based picture fuzzy topsıs method. International Journal of Automotive Science and Technology, 9(2), 230-240. https://doi.org/10.30939/ijastech..1639635
32. Das, A. (2025). Evaluation of Surface Water Quality in Mahanadi River Basin, Odisha, for Drinking Purposes Based on GIS, MEREC and a Hybrid MACROS Approach. In: Surface, Sub-Surface Hydrology and Management, Pal, S.C., Chatterjee, U. (ed.), Springer, Berlin, 625-655. https://doi.org/10.1007/978-3-031-62376-9_27
33. Dhal, P. R., Choudhury, B. B., & Sahoo, S. K. (2024). Evaluating motor choices for a smart wheelchair prototype using an integrated TODIM-CoCoSo approach with MEREC weighting. Engineering Review, 44(4), 22-44. https://doi.org/10.30765/er.2610
34. Ertuğrul, M., & Özdarak, E. (2025). Measuring airline performance: an ıntegrated balanced scorecard-based merec-cocoso model. Sustainability, 17(3), 1-25. https://doi.org/10.3390/su17135826
35. Khanam, S., Khan, O., Ahmad, S., Sherwani, A. F., Khan, Z. A., & Yadav, A. K. (2024). A Taguchi-based hybrid multi-criteria decision-making approach for optimization of performance characteristics of diesel engine fuelled with blends of biodiesel-diesel and cerium oxide nano-additive. Journal of Thermal Analysis and Calorimetry, 149, 3657–3676. https://doi.org/10.1007/s10973-024-12918-x
36. Timm, N. H. (1971). Neyman's Restricted Chi-Square Tests (*Presented at the American Educational Research Association Annual fleeting). University of Pittsburgh, New York.
37. Loisel, S., & Takane, Y. (2022). An algebraic theory of contrasts for Neyman’s modified chi-square statistic. Behaviormetrika, 50(1), 335-360.
38. Neyman, J. (1949). Contribution to the Theory of the {χ superscript 2} Test. Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, August, 1945 and January, 1946, Berkeley, University of California Press, 239-273.
39. Levy, A., Shalom, B. R., & Chalamish, M. (2024). A Guide to similarity measures. arXiv, 2408.0770, 1-27. https://doi.org/10.48550/arXiv:2408.0770.
40. Markatou, M., Chen, Y., Afendras, G., & Lindsay, B. G. (2017). Statistical distances and their role in robustness. In: Chen, DG., Jin, Z., Li, G., Li, Y., Liu, A., Zhao, Y. (ed), New Advances in Statistics and Data Science. ICSA Book Series in Statistics, Springer, Berlin, 3-26. https://doi.org/10.1007/978-3-319-69416-0_1
41. Agresti, A. (2023). Categorical data analysis. John Wiley & Sons, New Jersey.
42. Gaunt, R. E. (2021). Bounds for the chi-square approximation of the power divergence family of statistics. arXiv, 2107.00535, 1-26. https://doi.org/10.485550/arXiv.2107.00535
43. Beh, E. J., & Lombardo, R. (2022). Correspondence Analysis and the cressie-read (Working Paper 06-22). Wollongong: University of Wollongong.
44. Govindaraj, S., & Tejas, T. (2022). The Hellinger distance and its applications to hypothesis testing and model uncertainty. SSRN, 1-39. https://dx.doi.org/10.2139/ssrn.4035007
45. Deza, M. M., & Deza, E. (2009). Encyclopedia of Distances. Springer-Verlag, Berlin, Heidelberg.
46. Cha, S.-H. (2007). Comprehensive survey on distance/similarity measures between probability density functions. International Journal of Mathematical Models And Methods in Applied Sciences, 4(1), 300-307.
47. Broniatowski, M., & Leorato, S. (2006). An estimation method for the Neyman chi-square divergence between distributions. Journal of Multivariate Analysis, 97(1), 1–20. https://doi.org/10.1016/j.jmva.2005.01.010
48. Ji, X., Gu, W., Qian, X., Wei, H., & Zhang, C. (2020). Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square. Nuclear Instruments and Methods in Physics Research A, 961, 163677. https://doi.org/10.1016/j.nima.2020.163677
49. Chen, C.-H., Lai, C.-Y., & Ying, Z. (2004). Goodness-of-fit tests for grouped survival data based on the power-divergence family. Statistica Sinica, 14(3), 789–808.
50. Beh, E. J. (2024). On the role of the Cressie–Read family in analysing departures from independence. International Statistical Review, 92(1), 1–25. https://doi.org/10.1111/insr.12500
51. Nishiyama, T., & Sason, I. (2020). On relations between the relative entropy and χ²-divergence. Entropy, 22(12), 1407. https://doi.org/10.3390/e22121407
52. Nielsen, F., & Nock, R. (2013). On the chi-square and higher-order chi distances for approximating f-divergences. arXiv preprint arXiv:1309.3029
53. Forthofer, R. N. (1973). Minimum modified chi-square estimation in compounded function models. Biometrika, 60(3), 531–538. https://doi.org/10.1093/biomet/60.3.531
54. Şahin, M. (2023). Çok Kriterli Karar Verme Kriter Ağırlıklandırma Yöntemleri. Nobel Akademik, Ankara
55. Yılmaz, B. (2025). Determining the digitalization levels of leading countries in logistics performance ındex: An Application with CRITIC-TOPSIS Approach. Verimlilik Dergisi, 59(2), 433-452. https://doi.org/10.51551/verimlilik.1541480
56. Eşiyok, S., & Antmen, F. Z. (2025). Determination of renewable energy growth using cluster analysis and multi-criteria decision-making methods. applied sciences, 15(3), 1-19. https://doi.org/10.3390/app15031575.
57. Nasser, A. A., Alghawli, A. S., Saleh, S., & Elsayed, A. A. (2025). Income-based analysis of health security in Western Asia through an integrated GHSI, MCDM, and Clustering. F1000Research, 14(43), 1-26. https://doi.org/10.12688/f1000research.159002.2
58. Demir, G., Özyalçın, A. T., & Bircan, H. (2021). Çok kriterli karar verme yöntemleri ve ÇKKV yazılımı ile problem çözümü. Nobel, Ankara.
59. İnkaya, A., & Masca, M. (2025). Analysis of Agricultural Performance of BRICS Countries and Türkiye with CRITIC-Based Grey Relational Analysis Method. Journal of Research in Economics, Politics & Finance, 10(2), 596-618. https://doi.org/10.30784/epfad.1635472
60. Ulutaş, A., & Topal, A. (2020). Bütünleştirilmiş çok kriterli karar verme yöntemlerinin üretim sektörü uygulamaları. Akademisyen Kitapevi, Ankara.
61. Uludağ, A. S., & Doğan, H. (2021). Üretim yönetiminde çok kriterli karar verme yöntemleri. Nobel Yayıncılık, Ankara.
62. Pelit, I., & Avşar, I. İ. (2025). Turkiye’s carbon emission profile: a global analysis with the merec-promethee hybrid method. Sustainability, 17(14), 1-22. https://doi.org/10.3390/su17146527
63. World Intellectual Property Organization (WIPO. (2024). Global innovation ındex 2024: Unlocking the Promise of Social Entrepreneurship. WIPO, Geneva
64. World Competitiveness Center (WCC). (2024). IMD World Competitiveness Booklet 2024. Lausanne: International Institute for Management Development.
65. Sachs, J. D., Lafortune, G., Fuller, G., & Iablonovski, G. (2025). Financing Sustainable Development to 2030 and Mid-Century. Sustainable Development Report 2025. Dublin: Dublin University Press.
66. Demir, G., & Arslan, R. (2022). Sensitivity analysis in multi-criteria decision-making problems. Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 24(3), 1025-1056. https://doi.org/10.26745/ahbvuibfd.1103531
67. Alpar, R. (2017). Uygulamalı çok değişkenli istatistiksel yöntemler. Detay Yayıncılık, Ankara.
68. Karagöz, Y. (2019). SPSS - AMOS - META uygulamalı istatistiksel analizler. Nobel Akademik, Ankara.