A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)

Furkan Fahri Altıntaş

doi:10.30855/gmbd.070526A04

A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)

Abstract

In multi-criteria decision-making (MCDM) problems, most objective weighting methods focus either solely on internal variability (e.g., ENTROPY, SD, SVP, LOPCOW) or exclusively on external structural interactions (e.g., MEREC). Although CRITIC considers both aspects, it remains limited to linear relationships and parametric assumptions, such as normal distribution. This methodological gap significantly compromises decision quality, serving as the primary motivation for this study. In response, this research proposes the Squared Chord Distance Method (SCDM), a novel approach that simultaneously incorporates both internal and external structural divergence in a non-parametric framework. While internal variation is quantified through standard deviation, external distributional differences are captured using the Squared Chord Distance metric independent of correlation-based assumptions. Sensitivity analysis demonstrates the robustness of SCDM against weight perturbations; comparative evaluation confirms its alignment with widely accepted methods; and simulation results highlight its ability to generate balanced and stable weights. In this context, SCDM offers an original and methodologically sound contribution to the literature by embedding distributional distance analysis directly into the decision-making process.

Keywords

References

[1] N. Munier, Strategic Approach in Multi-Criteria Decision Making: A Practical Guide for Complex Scenarios. Heidelberg, Germany: Springer, 2024.
[2] M. Şahin, Çok Kriterli Karar Verme: Kriter Ağırlıklandırma Yöntemleri. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2023.
[3] F. Ecer, Çok Kriterli Karar Verme. Ankara, Türkiye: Seçkin Yayıncılık, 2020.
[4] E. Ayçin, Çok Kriterli Karar Verme. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2020.
[5] A. S. Uludağ and H. Doğan, Üretim Yönetiminde Çok Kriterli Karar Verme Yöntemleri: Literatür, Teori ve Uygulama. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2021.
[6] G. Demir, A. T. Özyalçın, and H. Bircan, Çok Kriterli Karar Verme Yöntemleri ve ÇKKV Yazılımı ile Problem Çözümü. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2021.
[7] F. Ecer and D. Pamucar, "A novel LOPCOW-DOBI multi-criteria sustainability performance assessment methodology: An application in developing country banking sector," Omega, vol. 112, Art. no. 102690, 2022. doi: 10.1016/j.omega.2022.102690
[8] M. Keshavarz-Ghorabaee, M. Amiri, E. K. Zavadskas, Z. Turskis, and J. Antucheviciene, "Determination of objective weights using a new method based on the removal effects of criteria (MEREC)," Symmetry, vol. 13, no. 4, Art. no. 525, 2021. doi: 10.3390/sym13040525

[9] M. Keshavarz-Ghorabaee, E. K. Zavadskas, L. Olfat, and Z. Turskis, "Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS)," Informatica, vol. 26, no. 3, pp. 435–451, 2015. doi: 10.15388/Informatica.2015.57
[10] N. H. Zardari, K. Ahmed, S. M. Shirazi, and Z. B. Yusop, Weighting Methods and Their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management. Heidelberg, Germany: Springer, 2014.
[11] J. T. Overpeck, T. Webb III, and I. C. Prentice, "Quantitative interpretation of fossil pollen spectra: Dissimilarity coefficients and the method of modern analogs," Quaternary Research, vol. 23, no. 1, pp. 87-108, 1985. doi: 10.1016/0033-5894(85)90074-2
[12] G. L. Simpson, "Analogue methods in palaeoecology: Using the analogue package," Journal of Statistical Software, vol. 22, no. 2, pp. 1-29, 2007. doi: 10.18637/jss.v022.i02
[13] F. Baş, Çok Kriterli Karar Verme Yöntemlerinde Kriter Ağırlıklarının Belirlenmesi. Ankara, Türkiye: Nobel Bilimsel Yayıncılık, 2021.
[14] H. Bircan, Çok Kriterli Karar Verme Problemlerinde Kriter Ağırlıklandırma Yöntemleri. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2020.
[15] M. Kabak, Ed., Çok Kriterli Karar Verme Yöntemleri: MS Excel Çözümlü Uygulamalar. Ankara, Türkiye: Nobel Akademik Yayıncılık, 2020, pp. 169-179.
[16] S. Zhao, H. Deng, and J. Steve, “Research on statistical measure under double carbon target: Self-moving regression model of grey prediction based on entropy weight method,” F1000Research, vol. 14, no. 437, pp. 1–25, 2025. doi: 10.12688/f1000research.162696.2
[17] P. Zheng and T. Qin, “Calculation and comprehensive evaluation of China's tourism high-quality development level and regional differences and dynamic evolution based on entropy weight method and TOPSIS modeling,” Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 127, pp. 6243–6265, 2025.
[18] G. O. Odu, “Weighting methods for multi-criteria decision making technique,” Journal of Applied Sciences and Environmental Management, vol. 23, no. 8, pp. 1449–1457, 2019. doi: 10.4314/jasem.v23i8.7
[19] I. Z. Mukhametzyanov, “Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC, and SD,” Decision Making: Applications in Management and Engineering, vol. 4, no. 2, pp. 76–105, 2021. doi: 10.31181/dmame210402076i
[20] A. Öztel and İ. Alp, Çok Kriterli Karar Verme Yöntemi Seçiminde Yeni Bir Yaklaşım. İstanbul, Türkiye: Kriter Yayıncılık, 2020.
[21] A. A. Nasser, N. A. Mansoor, A. A. Alkhulaidi, M. Hankal, and M. Al-Olofe, “A weighted Euclidean distance-statistical variance procedure based approach for improving the healthcare decision making system in Yemen,” Indian Journal of Science and Technology, vol. 12, no. 3, pp. 1–15, 2019. doi: 10.17485/ijst/2019/v12i3/140661
[22] H. A. Tayalı and M. Timor, “Ranking with statistical variance procedure based analytic hierarchy process,” Acta Infologica, vol. 1, no. 1, pp. 31–38, 2017.
[23] D. Durdu, “Evaluating financial performance with SPC-LOPCOW-MARCOS hybrid methodology: A case study for firms listed in BIST Sustainability Index,” Knowledge and Decision Systems with Applications, vol. 1, pp. 92–111, 2025.
[24] A. A. Yürüyen and A. Ulutaş, “Assessing the urban competitiveness of European cities using LOPCOW-RAWEC methodologies,” International Journal of Knowledge and Innovation Studies, vol. 2, no. 3, pp. 179–189, 2024. doi: 10.56578/ijkis020305
[25] Setiawansyah, “Improving decision accuracy through LOPCOW weighting and AROMAN methods in retail store location selection,” Jurnal Ilmiah Informatika dan Ilmu Komputer (JIMA-ILKOM), vol. 4, no. 1, pp. 77–88, 2025. doi: 10.58602/jima-ilkom.v4i1.57
[26] S. Paksoy, Çok Kriterli Karar Vermede Güncel Yaklaşımlar. Adana, Türkiye: Karahan Kitabevi, 2017.
[27] M. E. Akpınar, “Analysis of Logistics 4.0 service provider alternatives with CRITIC-based WASPAS method,” Verimlilik Dergisi, Special Issue: Productivity for Logistics, pp. 77–88, 2025.
[28] N. Keleş, Uygulamalarla Klasik ve Güncel Karar Verme Yöntemleri. Ankara, Türkiye: Atlas Akademik Basım Yayın Dağıtım, 2023.
[29] S. H. Zolfani, “Objective weighting in MCDM: A comparative study of CRITIC, ITARA, MEREC, and beyond,” Decision Making and Artificial Intelligence Trends, vol. 1, no. 1, pp. 105–120, 2024. doi: 10.22034/dmait.2024.488347.1007
[30] A. Elsayed, “Multi-criteria decision-making framework for evaluating green fuels alternatives: A hybrid MEREC-TODIM approach,” Neutrosophic Optimization and Intelligent Systems, vol. 3, pp. 41–56, 2024. doi: 10.61356/j.nois.2024.3323
[31] P. Legendre and L. Legendre, Numerical Ecology. Amsterdam, The Netherlands: Elsevier, 2012.
[32] D. G. Gavin, W. W. Oswald, E. R. Wahl, and J. W. Williams, A Statistical Approach to Evaluating Distance Metrics and Analog Assignments for Pollen Records. Cambridge, UK: Cambridge University Press, 2017.
[33] S. H. Cha, “Comprehensive survey on distance/similarity measures between probability density functions,” International Journal of Mathematical Models and Methods in Applied Sciences, vol. 4, no. 1, pp. 300–307, 2007.
[34] A. S. Shirkhorshidi, S. Aghabozorgi, and T. Y. Wah, “A comparison study on similarity and dissimilarity measures in clustering continuous data,” PLoS ONE, vol. 10, no. 12, pp. 1–20, 2015. doi: 10.1371/journal.pone.0144059
[35] A. Levy, B. R. Shalom, and M. Chalamish, “A guide to similarity measures,” arXiv, vol. 2408.0770, pp. 1–27, 2024. doi: 10.48550/arXiv.2408.0770
[36] J. Paparrizos, H. Li, F. Yang, K. Wu, J. E. D’Hondt, and O. Papapetrou, “A survey on time-series distance measures,” arXiv, vol. 2412.20574, pp. 1–42, 2024. doi: 10.48550/arXiv.2412.20574
[37] P. Legendre and M. D. Cáceres, “Beta diversity as the variance of community data: Dissimilarity coefficients and partitioning,” Ecology Letters, vol. 16, no. 8, pp. 951–963, 2013. doi: 10.1111/ele.12141
[38] H. G. Drost, “Package ‘philentropy’: Squared chi-squared distance (low-level function),” July 2023. [Online]. Available: https://cran.r-project.org/web/packages/philentropy/philentropy.pdf. [Accessed: Jul. 8, 2025].
[39] M. Muhaimin, A. Y. Chaerunisaa, and R. Bodmeier, “Real-time particle size analysis using focused beam reflectance measurement as a process analytical technology tool for a continuous microencapsulation process,” Research Square, pp. 1–18, 2021. doi: 10.21203/rs.3.rs-490815/v1
[40] H. J. Dowsett and M. M. Robinson, “Application of the modern analog technique (MAT) of sea surface temperature estimation to middle Pliocene North Pacific planktonic foraminifer assemblages,” Palaeontologia Electronica, vol. 1, no. 1, Art. no. 3A, pp. 1–22, 1997. doi: 10.26879/98003
[41] K. Gajewski, “Quantitative reconstruction of Holocene temperatures across the Canadian Arctic and Greenland,” Global and Planetary Change, vol. 128, pp. 14–23, 2015. doi: 10.1016/j.gloplacha.2015.02.003
[42] C. L. Hwang and K. Yoon, Multiple Attribute Decision Making: Methods and Applications. New York, NY, USA: Springer-Verlag, 1981.
[43] R. Alpar, Uygulamalı Çok Değişkenli İstatistiksel Yöntemler. Ankara, Türkiye: Detay Yayıncılık, 2020.
[44] Ş. Kalaycı, SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri. Ankara, Türkiye: Anı Yayın Dağıtım, 2013.
[45] World Intellectual Property Organization (WIPO), Global Innovation Index 2024: Unlocking the Promise of Social Entrepreneurship. Geneva, Switzerland: WIPO, 2024.
[46] J. D. Sachs, G. Lafortune, G. Fuller, and G. Iablonovski, Financing Sustainable Development to 2030 and Mid-Century: Sustainable Development Report 2025. Paris, France: SDSN; Dublin, Ireland: Dublin University Press, 2025. doi: 10.25546/111909
[47] S. Block, J. W. Emerson, D. C. Esty, A. de Sherbinin, Z. A. Wendling, et al., 2024 Environmental Performance Index. New Haven, CT, USA: Yale Center for Environmental Law & Policy, 2024.
[48] G. Demir and R. Arslan, “Sensitivity analysis in multi-criteria decision-making problems,” Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 24, no. 3, pp. 1025–1056, 2022.

Details

Primary Language

English

Subjects

Manufacturing and Industrial Engineering (Other)

Journal Section

Research Article

Authors

Furkan Fahri Altıntaş ^*
0000-0002-0161-5862
Türkiye

Publication Date

August 31, 2026

Submission Date

July 23, 2025

Acceptance Date

June 23, 2026

Published in Issue

Year 2026 Volume: 12 Number: 2

DOI

https://doi.org/10.30855/gmbd.070526A04

IZ

https://izlik.org/JA29UZ79EE

Cite

RIS / Bibtex

APA

Altıntaş, F. F. (2026). A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM). Gazi Journal of Engineering Sciences, 12(2), 169-200. https://doi.org/10.30855/gmbd.070526A04

AMA

1.Altıntaş FF. A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM). GJES. 2026;12(2):169-200. doi:10.30855/gmbd.070526A04

Chicago

Altıntaş, Furkan Fahri. 2026. “A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)”. Gazi Journal of Engineering Sciences 12 (2): 169-200. https://doi.org/10.30855/gmbd.070526A04.

EndNote

Altıntaş FF (August 1, 2026) A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM). Gazi Journal of Engineering Sciences 12 2 169–200.

IEEE

[1]F. F. Altıntaş, “A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)”, GJES, vol. 12, no. 2, pp. 169–200, Aug. 2026, doi: 10.30855/gmbd.070526A04.

ISNAD

Altıntaş, Furkan Fahri. “A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)”. Gazi Journal of Engineering Sciences 12/2 (August 1, 2026): 169-200. https://doi.org/10.30855/gmbd.070526A04.

JAMA

1.Altıntaş FF. A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM). GJES. 2026;12:169–200.

MLA

Altıntaş, Furkan Fahri. “A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM)”. Gazi Journal of Engineering Sciences, vol. 12, no. 2, Aug. 2026, pp. 169-00, doi:10.30855/gmbd.070526A04.

Vancouver

1.Furkan Fahri Altıntaş. A Novel Distribution-Based Weighting Approach for Multi-Criteria Decision-Making Problems: The Squared Chord Distance Method (SCDM). GJES. 2026 Aug. 1;12(2):169-200. doi:10.30855/gmbd.070526A04