A Novel Method for Objective Weighting in MCDM: The Lorentzian Distance Approach (LDA) Model

Öz

The objective determination of criterion weights in Multi-Criteria Decision-Making (MCDM) processes is of critical importance for ensuring the validity and reliability of decision outcomes. However, most existing methods primarily focus on internal variations or linear relationships among criteria, often overlooking external distributional effects and complex interdependencies. To address these methodological limitations, this study introduces an innovative framework the Lorentzian Distance Approach (LDA) which simultaneously considers both internal and external distributions of criteria. LDA statistically models the normalized distributions of criteria and employs the Lorentzian distance metric to measure inter-criterion divergence with high sensitivity. Empirical analyses conducted on the 2024 Global Innovation Index (GII) dataset (Criteria: Institutions, Human Capital and Research, Infrastructure, Market Sophistication, Business Sophistication, Knowledge and Technology Outputs, Creative Outputs; Alternatives: Indonesia, Mauritius, Mexico, Georgia, North Macedonia, Russian Federation, Ukraine) revealed that LDA demonstrates strong consistency and robustness in maintaining alternative rankings. In the rank reversal analysis, LDA exhibited a high degree of structural alignment with the ENTROPY (rho = 0.964, p < 0.01) and SVP (rho = 0.964, p < 0.01) methods. Furthermore, case studies based on the World Competitiveness Booklet and the Global Sustainable Index confirmed that LDA maintains ranking stability and preserves its homogeneous structure throughout simulation analyses. The selected datasets were chosen for their qualitative representation of global and international characteristics and their quantitative suitability, ensuring that no dominant criterion values existed among countries. In conclusion, the LDA method emerges as a methodologically robust, flexible, and adaptable approach, offering a compelling alternative to classical weighting models and demonstrating strong potential for application in decision-making environments under uncertainty.

Anahtar Kelimeler

• Lorentzian distance
• criteria weights
• LDA

ÇKKV’de Nesnel Ağırlıklandırma için Yeni Bir Yöntem: Lorentzian Uzaklık Yaklaşımı (LDA) Modeli

Öz

Çok Kriterli Karar Verme (ÇKKV) problemlerinde kriter ağırlıklarının nesnel olarak belirlenmesi, karar sürecinin doğruluk ve güvenilirliği açısından kritik bir öneme sahiptir. Ancak mevcut yöntemlerin büyük çoğunluğu, yalnızca kriterlerin içsel varyasyonlarına, sınırlı düzeydeki dışsal ilişkilerine veya kriterler arasındaki doğrusal korelasyonlara odaklanmaktadır. Bu metodolojik kısıtları aşmak amacıyla, bu çalışmada hem kriterlerin içsel hem de dışsal dağılımlarını eş zamanlı olarak dikkate alan özgün bir çerçeve olan Lorentzian Uzaklık Yaklaşımı (LDA) önerilmektedir. LDA, kriterlerin normalize edilmiş dağılımlarını istatistiksel olarak modellemekte ve kriterler arası ayrışmayı yüksek duyarlılıkla ölçmek için Lorentzian uzaklık metriğini kullanmaktadır. Yapılan duyarlılık analizleri, LDA’nın alternatif sıralamalarında tutarlılığını koruduğunu ve bu yönüyle yüksek düzeyde sağlamlık sergilediğini ortaya koymaktadır. Karşılaştırmalı değerlendirmeler, LDA ile ENTROPY ve SVP gibi yerleşik yöntemler arasında güçlü yapısal uyum bulunduğunu, aynı zamanda LDA’nın diğer tekniklerden belirgin şekilde ayrıştığını göstermektedir. Simülasyon sonuçları ise, veri karmaşıklığı arttığında dahi yöntemin istikrarlı çıktılar üretebildiğini doğrulamaktadır. Dolayısıyla, LDA klasik ağırlıklandırma yaklaşımlarına güçlü, metodolojik olarak sağlam ve güvenilir bir alternatif sunmakta olup, belirsizlik içeren karar verme ortamlarına uyarlanabilmesi açısından da önemli bir potansiyele sahiptir.

Anahtar Kelimeler

• Lorentzian distance
• criteria weights
• LDA

Kaynakça

1. [1] Lopez, L. M., Ishizaka, A., Qin, J., “Multi Criteria Decision Making Sorting Methods: Applications to Real World”, Cambridge-Massachusetts: Academic Press (2023).
2. [2] Thakkar, J. J., “Multi Criteria Decision Making”, Singapore: Springer Singapore (2021).
3. [3] Munier, N., “Strategic Approach in Multi Criteria Decision Making”, Gewerbestrasse: Springer International Publishing AG (2024).
4. [4] Zardari, N. H., Ahmed, K., Shirazi, S. M., Yusop, Z. B., “Weighting Methods and their Effects on Multi Criteria Decision Making Model Outcomes in Water Resources Management”, Berlin: Springer Nature (2014).
5. [5] Ayçin, E., “Çok Kriterli Karar Verme”, Ankara: Nobel Yayın (2019).
6. [6] Dinçer, S. E., “Çok Kriterli Karar Alma”, Ankara: Gece Akademi (2019).
7. [7] Tayalı, H. A., Timor, M., “Ranking with Statistical Variance Procedure Based Analytic Hierarchy Process”, Acta Infologica 1(1) (2017): 31-38.
8. [8] Ecer, F., Pamucar, D., “A Novel LOPCOW‐DOBI Multi‐Criteria Sustainability Performance Assessment Methodology: An Application in Developing Country Banking Sector“, Omega 112 (2022): 102690.

9. [9] Diakoulaki, D., Mavrotas, G., Papayannakis, L., “Determining Objective Weights in Multiple Criteria Problems: The Critic Method“, Computers & Operations Research 22(7) (1995): 763-770.
10. [10] Kalaycı, Ş., “SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri”, Ankara: Asil Yayıncılık (2024).
11. [11] Alpar, R., “Uygulamalı Çok Değişkenli İstatistiksel Yöntemler”, Ankara: Detay Yayıncılık (2020).
12. [12] Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., Antucheviciene, J., “Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC)“, Symmetry 13 (2021) : 1-21.
13. [13] Cha, S.-H. Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions. International Journal of Mathematical Models And Methods in Applied Sciences, 4(1) (2007) : 300-307.
14. [14] Kerimbekov, Y., Bilge, H. Ş., Uğurlu, H. H., “The Use of Lorentzian Distance Metric in Classification Problems”, Pattern Recognition Letters 84 (2016) : 170-176.
15. [15] Özkeleş, B,. ''Medium. Machine Learning — Distance Metrics'', (2025). https://medium.com/@burak.ozkeles/machine-learning-distance-metrics-b00dc7ac17df (05/11/2025).
16. [16] World Intellectual Property Organization (WIPO)., “Global Innovation Index 2024: Unlocking the Promise of Social Entrepreneurship”, Geneva: WIPO (2024).
17. [17] World Competitiveness Center (WCC). IMD World Competitiveness Booklet 2024. Lausanne: International Institute for Management Development (2024).
18. [18] Sachs, J. D., Lafortune, G., Fuller, G., Iablonovski, G., Financing Sustainable Development to 2030 and Mid-Century. Sustainable Development Report 2025. Dublin: Dublin University Press (2025).
19. [19] Ecer, F., “Çok Kriterli Karar Verme”, Ankara: Seçkin Yayıncılık (2020).
20. [20] Bircan, H., “Çok Kriterli Karar Verme Problemlerinde Kriter Ağırlıklandırma Yöntemleri”, Ankara: Nobel Akademik Yayıncılık (2020).
21. [21] Ulutaş, A., Topal, A., “Bütünleştirilmiş Çok Kriterli Karar Verme Yöntemlerinin Üretim Sektörü Uygulamaları”, Ankara: Akademisyen Kitapevi (2020).
22. [22] Şahin, M., “Çok Kriterli Karar Verme Kriter Ağırlıklandırma Yöntemleri”, Ankara: Nobel Akademik (2023).
23. [23] Dasgupta, A., Sen, B., Karthikeyan, A., Dutta, P., Rachchh, N., Patil, N., Mahapatro, A., “Entropy-TOPSIS-based Material Selection for Sustainable Polymer Composite: An MCDM Framework Promoting Circular Economy”, Journal of Elastomers & Plastics 57(5) (2025) : 703-729.
24. [24] Salaj, Kumari, M., “A Multi-Criteria Approach to Blockchain in Supply Chain Management Assessment: Entropy-CRITIC Weight Method and MCDM for Enhanced Decision Support”, International Journal of System Assurance Engineering and Management 16 (2025) : 1830–1843.
25. [25] Doğan, H., Uludağ, A. S.,. ''Üretim Yönetiminde Çok Kriterli Karar Verme Yöntemleri: Literatür, Teori ve Uygulama'', Ankara: Nobel Akademik Yayıncılık (2021).
26. [26] Mukhametzyanov, I., “Specific Character Of Objective Methods for Determining Weights of Criteria in MCDM Problems: Entropy, CRITIC and SD Decision Making”, Applications in Management and Engineering 4(2) (2021) : 76-105.
27. [27] Anitha, J., Das, R., “Optimization of EDM Process Parameters Using Standard Deviation and Multi-objective Optimization on the Basis of Simple Ratio Analysis (MOOSRA)”, In: Reddy, A., Marla, D., Simic, M., Favorskaya, M., Satapathy, S. (eds), Intelligent Manufacturing and Energy Sustainability, Smart Innovation, Systems and Technologies 16 (2020): 655–662. Singapore: Springer. https://doi.org/10.1007/978-981-15-1616-0_63
28. [28] Odu, G. 0., “Weighting Methods for Multi-Criteria Decision Making Technique”, J. Appl. Sci. Environ. Manage 23(8) (2019):1449-1457.
29. [29] Öztel, A., Alp, İ., “Çok Kriterli Karar Verme Seçiminde Yeni Bir Yaklaşım”, İstanbul: Kriter Yayıncılık (2020).
30. [30] Demir, G., Özyalçın, A. T., Bircan, H., “Çok Kriterli Karar Verme Yöntemleri ve ÇKKV Yazılımı ile Problem Çözümü”, Ankara: Nobel (2021).
31. [31] Özbek, A., Aydın, Ş. N., “Çok Kriterli Karar Verme Yöntemleri ve Excel ile Problem Çözümü Kavram – Teori – Uygulama”, Ankara: Seçkin Yayıncılık (2021).
32. [32] Keleş, N., “Uygulamalarla Klasik ve Güncel Karar Verme Yöntemleri”, Ankara: Atlas Akademik Basım Yayın Dağıtım (2023).
33. [33] Dey, S., Mitra, G., Biswas, S., Pamucar, D., “Evaluation of Fim Performance under Merger and Acquisition Effect: An Integrated LOPCOW-PIV Approach”, Decision Making: Applications in Management and Engineering 8(1) (2025) : 588–614.
34. [34] Setiawansyah. ''Improving Decision Accuracy Through LOPCOW Weighting and AROMAN Methods in Retail Store Location Selection'', Jurnal Ilmiah Informatika Dan Ilmu Komputer (Jima-Ilkom), 4(1), (2025) : 77-88. https://doi.org/10.58602/jima-ilkom.v4i1.57
35. [35] Demir, G., Kartal, M., “Güncel Çok Kriterli Karar Verme Teknikleri”, Ankara: Akademisyen Yayınevi (2020).
36. [36] Coşansu, D. T., “Personel Seçiminde Çok Kriterli Karar Verme”, Bursa: Ekin Yayınevi (2023).
37. [37] Fan, J., Han, Y., Wu, M., “CRITIC-TOPSIS Method Based on Pairwise Preference Graph Neural Similarity and Its Application in Vehicle Selection”, J. Fuzzy Syst (2025).
38. [38] Sultana, M., Sarker, O. S., Dhar, N. R., “Parametric Optimization and Sensitivity Analysis of the İntegrated Taguchi-CRITIC-EDAS Method to Enhance The Surface Quality and Tensile Test Behavior of 3D Printed PLA and ABS Parts”, Heliyon 11 (2025): 1-18.
39. [39] Zolfani, S. H., “Objective Weighting in MCDM: A Comparative Study of CRITIC, ITARA, MEREC, and Beyond, Decision Making and Artificial Intelligence Trends”, 1(1) (2024) : 105-120.
40. [40] Kumar, S., Kumar, P. A., Bharati, K., Patnaik, L., Maity, S. R., Łepicka, M., “Coating Material Selection for Bulk Metal Forming Dies: A MEREC-Integrated Approach with Multiple MCDM Methods”, International Journal on Interactive Design and Manufacturing (IJIDeM) 19 (2025) : 4055 4070.
41. [41] Jameel, T., Yasin, Y., Riaz, M., “An Integrated Hybrid MCDM Framework for Renewable Energy Prioritization in Sustainable Development”, Spectrum of Decision Making and Applications 3(1) (2025) : 124-150.
42. [42] Wang, C. N., Nguyen, H. K., Nhieu, N.L., “Assessing Sustainability on The Modern Silk Road: An Objective Weighting Methodological Approach”, PLOS one 20(5) (2025) : 1-20.
43. [43] Wang, J., Darwis, D., Gunawan, R. D., Ariany, F., “Optimizing E-Commerce Platform Selection Using Root Assessment Method and MEREC Weighting”, Jurnal Informatika Dan Rekayasa Perangkat Lunak (Jatika) 6(1) (2025) : 1-12.
44. [44] Zavadskas, E. K., Antucheviciene, J., Podvezko, V., ''Integrated determination of objective criteria weights in MCDM based on CILOS and IDOCRIW methods'', Technological and Economic Development of Economy'', 23(1) (2017) : 1–19.
45. [45] Hatefi, M. A., ''Indifference threshold-based attribute ratio analysis (ITARA): A method for assigning weights to attributes in MCDM'', Applied Soft Computing, 74 (2019) : 643–651.
46. [46] Paradowski, B., Shekhovtsov, A., Bączkiewicz, A., Kizielewicz, B., Sałabun, W., ''Similarity analysis of methods for objective determination of weights in MCDM'', Symmetry, 13(10) (2021) : 1874-1885.
47. [47] Ayan, B., Abacıoğlu, S., Basilio, M. P., ''A comprehensive review of novel weighting methods for multi-criteria decision-making. Information'', 14(5) (2023) : 285-300
48. [48] Chatterjee, S., Chakraborty, S., ''A study on the effects of objective weighting methods on TOPSIS-based parametric optimization of non-traditional machining processes'', Decision Analytics Journal, 11 (2024).
49. [49] Van Dua, T., Van Duc, D., Bao, N. C., Trung, D. D., ''Integration of objective weighting methods for criteria and MCDM: Application in material selection'', EUREKA: Physics and Engineering, (2) (2024) : 131–148.
50. [50] Linh, N. T. D., Son, N. H., Thao, D. X., ''Evaluating the impact of weighting methods on the stability of scores for alternatives in MCDM problems'', Engineering, Technology & Applied Science Research, 15(1) (2025) : 19998–20004.
51. [51] Kizielewicz, B., Sałabun, W., ''SITW method: A new approach to re-identifying multi-criteria weights in complex decision analysis,'' Spectrum of Mechanical Engineering and Operational Research, 1(1) (2024) : 215–226.
52. [52] Minguzzi, E., “Characterization of Some Causality Conditions through the Continuity Of The Lorentzian Distance”, arXiv 0810.1879v3 (2008) : 1-14.
53. [53] Beem, J. K., Ehrlich, P., Easley, K., “Global Lorentzian Geometry”, New York: MARCEL DEKKER INC (1996).
54. [54] Minguzzi, E., Sanchez, M., “The Causal Hierarchy of Spacetimes”, arXiv (2008) : 1-63.
55. [55] Kunzinger, M., Sämann, C., “Lorentzian Length Spaces, Annals of Global Analysis and Geometry 54 (2018) : 399–447.
56. [56] O’neill, B., “Semi-Riemannian Geometry with Applications to Relativity”, London: Academic Press (1983).
57. [57] Sachs, R. K., Wu, H. H., “General Relativity for Mathematicians”, Berlin: Springer Verlag (1977).
58. [58] Bernal, A., Sánchez, M., “Smoothness of Time Functions and The Metric Splitting of Globally Hyperbolic Spacetimes”, Communications in Mathematical Physics 257 (2005) : 43–50.
59. [59] Levy,, A., Shalom, R., Chalamish, M., “A Guide to Similarity Measures”, arXiv 2408.07706 (2024) : 1-27.
60. [60] Bilge, H. Ş., Kerimbekov, Y., Uğurlu, H. H., “A New Classification Method by Using Lorentzian Distance Metric”, International Symposium on Innovations in Intelligent SysTems and Applications (INISTA 2015) Madrid, Spain (2015).
61. [61] TradingView. (2023). Machine Learning Lorentzian Classification, Retrieved on the 8/8/2025 from: https://www.tradingview.com/script/WhBzgfDu-Machine-Learning-Lorentzian-Classification/
62. [62] Nickel, M., Kiela, D., ''Poincaré Embeddings for Learning Hierarchical Representations'', 31st Conference on Neural Information Processing Systems (NIPS 2017) (2017) :1-10. Long Beach, CA, USA.: NeurIPS Proceedings.
63. [63] Belkin, M., Niyogi, P., “Laplacian eigenmaps for dimensionality reduction and data representation”, Neural Computation 15(6) (2003) : 1373–1396.
64. [64] Wilson, D. R., Martinez, T. R., “Improved heterogeneous distance functions”, Journal of Artificial Intelligence Research 6 (1997) : 1–34.
65. [65] Demir, G., Arslan, R., “Sensitivity Analysis in Multi-Criteria Decision-Making Problems”, Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 24(3) (2022) : 1025-1056.
66. [66] Jain, A. K., “Data clustering: 50 years beyond K-means”, Pattern Recognition Letters 31(8) (2010) : 651–666.
67. [67] Iglewicz, B., Hoaglin, D., “How to detect and handle outliers”, Milwaukee: ASQC Quality Press (1993).
68. [68] Hwang, C. L., Yoon, K., “Multiple Attribute Decision Making: Methods and Applications”, Berlin: Springer (1981).
69. [69] Zavadskas, E. K., Turskis, Z., “A new additive ratio assessment (ARAS) method”, Technological and Economic Development of Economy 16(2) (2010) : 159–172.
70. [70] Box, G. E. P., Cox, D. R., “An analysis of transformations”, Journal of the Royal Statistical Society Series B 26(2) (1964) : 211–252.
71. [71] Kuo, R. J., Chi, S. C., Kao, S. S., “A decision support system for selecting convenience store location”, Computers in Industry 47(2) (2002) : 199–214.
72. [72] Bishop, C. M., “Pattern Recognition and Machine Learning”, New York: Springer (2006).