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A CURRENT APPROACH TO OBJECTIVE CRITERIA WEIGHTING: THE HELLINGER DISTANCE METHOD (HDM)

Year 2025, Volume: 28 Issue: 4, 1861 - 1885, 03.12.2025

Furkan Fahri Altıntaş

Abstract

This study introduces the Hellinger Distance Method (HDM), a novel objective weighting approach for multi-criteria decision-making (MCDM) problems. HDM employs a dual-layered structure by simultaneously accounting for the internal variation of each criterion (via standard deviation) and the distributional dissimilarities between criteria (via the Hellinger Distance). The method was applied to assess innovation performance across seven countries using the 2024 Global Innovation Index data. Rank Reversal analysis demonstrated that HDM maintains stable alternative rankings following systematic criterion removal, indicating robust sensitivity. Further comparisons with established objective weighting methods ENTROPY, CRITIC, SD, SVP, LOPCOW, and MEREC revealed strong alignment with ENTROPY and SVP, reinforcing HDM’s reliability and methodological soundness. In addition, simulation-based analyses involving ten decision matrix scenarios confirmed the statistical homogeneity and stability of HDM-derived weights, as validated by ANOM and Levene’s tests. These findings highlight the method’s consistent performance across varied data conditions. Overall, HDM emerges as a reliable, theoretically grounded, and practically effective weighting technique, offering a valuable contribution to both the academic literature and real-world MCDM applications.

Keywords

MCDM Hellinger distance internal distribution external distribution HDM

References

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NESNEL KRİTER AĞIRLIKLANDIRMAYA GÜNCEL BİR YAKLAŞIM: HELLİNGER MESAFE YÖNTEMİ (HDM)

Year 2025, Volume: 28 Issue: 4, 1861 - 1885, 03.12.2025

Furkan Fahri Altıntaş

Abstract

Bu çalışma, çok kriterli karar verme (ÇKKV) problemleri için nesnel bir ağırlıklandırma yöntemi olan Hellinger Mesafe Yöntemi’ni (HDM) literatüre kazandırmaktadır. HDM, her bir kriterin içsel varyasyonunu (standart sapma) ve kriterler arasındaki dağılımsal farklılıkları (Hellinger Mesafesi) eş zamanlı dikkate alan iki katmanlı bir yapı sunmaktadır. Yöntem, 2024 Küresel İnovasyon Endeksi verileriyle yedi ülkenin inovasyon performanslarını değerlendirmek amacıyla uygulanmıştır. Duyarlılığı test etmek amacıyla gerçekleştirilen Sıra Terslenmesi analizinde, sistematik kriter çıkarımı sonrasında sıralamalarda anlamlı bir değişim gözlenmemiştir; bu durum HDM’nin kararlılığını göstermektedir. ENTROPY, CRITIC, SD, SVP, LOPCOW ve MEREC yöntemleriyle yapılan karşılaştırmalar, HDM’nin özellikle ENTROPY ve SVP ile yüksek uyum gösterdiğini ortaya koyarak güvenilirliğini doğrulamaktadır. On senaryolu simülasyon analizleri ise, ANOM ve Levene testleri aracılığıyla elde edilen ağırlıkların değişen veri setlerine rağmen istatistiksel olarak homojen kaldığını göstermektedir. Bulgular, HDM’nin farklı veri koşullarında dahi istikrarlı sonuçlar sunduğunu ve hem kuramsal hem de uygulamalı olarak güçlü bir katkı sağladığını göstermektedir.

Keywords

ÇKKV Hellinger mesafesi içsel dağılım dışsal dağılım HDM

References

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  • Alinezhad, A., & Khalili, J. (2019). New Methods and Applications in Multiple Attribute Decision Making (MADM). Heidelberg: Springer International Publishing.
  • Alpar, R. (2020). Uygulamalı Çok Değişkenli İstatistiksel Yöntemler. Ankara: Detay Yayıncılık.
  • Amimour, A., Belaide, K., & Hili, O. (2022). Minimum hellinger distance estimates for a periodically time-varying long memory parameter. Comptes Rendus Mathématique, 360, 1153-1162. https://doi.org/10.5802/crmath.381.
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  • Angadi, A., & Gorripati, S. K. (2025). A privacy preserving collaborative filtering approach using Hellinger distance similarity metric for high dimensional dataset. Home International Journal of Business Information Systems, 48(4), 555-572. https://doi.org/10.1504/IJBIS.2025.145569.
  • Asker, V., & Kılınç, Z. (2025). Financial and Operational Performance Analysis Using LOPCOW Based MARCOS Method: A Case Study of the Asian Airline Market. Journal of Mehmet Akif Ersoy University Economics and Administrative Sciences Faculty, 12(1), 246-270. https://doi.org/10.30798/makuiibf.1495165.
  • Ayçin, E. (2020). Çok Kriterli Karar Verme. Ankara: Nobel Akademik Yayıncılık.
  • Basu, A., Shioya, H., & Park, C. (2011). Statistical inference: The Minimum Distance Approach. Boca Raton: CRC Press.
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  • 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.
  • Demir, G., Özyalçın, A. T., & Bircan, H. (2021). Çok kriterli karar verme yöntemleri ve çkkv yazılımı ile problem çözümü. Ankara: Nobel Akademik Yayıncılık.
  • Deng, F., & Vidyashankar, A. N. (2025). Private minimum Hellinger distance estimation via Hellinger distance differential privacy, arXiv Preprint, 2501.14974, 1-71. https://doi.org/10.48550/arXiv.2501.14974
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  • Ding, B., Karunamuni, R. J., & Wua, J. (2025). Minimum profile Hellinger distance estimation of general covariate models. Computational Statistics and Data Analysis, 202, 1-19. https://doi.org/10.1016/j.csda.2024.108054.
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  • Ditzler, G., & Polikar, R. (2011). Hellinger distance based drift detection for nonstationary environments. IEEE Symposium on Computational Intelligence in Dynamic and Uncertain Environments (CIDUE), (pp. 41-48. https://doi.org/ 10.1109/CIDUE.2011.5948491). Paris.
  • Doğan, H., & Uludağ, A. S. (2021). Üretim Yönetiminde Çok Kriterli Karar Verme Yöntemleri: Literatür, Teori ve Uygulama. Ankara: Nobel Akademik Yayıncılık.
  • Dwivedi, P. P., & Sharma, D. K. (2022). A pervasive model to evaluate and ranking the best 5g mobile by cross-entropy and topsis method. Comminication Systems, 38(4), 1-7. https://doi.org/10.1002/dac.6134.
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There are 75 citations in total.

Details

Primary Language English
Subjects Multiple Criteria Decision Making
Journal Section Research Article
Authors

Furkan Fahri Altıntaş 0000-0002-0161-5862

Publication Date December 3, 2025
Submission Date June 30, 2025
Acceptance Date September 19, 2025
Published in Issue Year 2025 Volume: 28 Issue: 4

Cite

APA Altıntaş, F. F. (2025). A CURRENT APPROACH TO OBJECTIVE CRITERIA WEIGHTING: THE HELLINGER DISTANCE METHOD (HDM). Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 28(4), 1861-1885.
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