journal article·2025-04-07Open access

Adaptive Cluster-Based Normalization for Robust TOPSIS in Multicriteria Decision-Making

Vitor Anes, António Abreu

Applied Sciences· Volume 15· Issue 7

Abstract

In multicriteria decision-making (MCDM), methods such as TOPSIS are essential for evaluating and comparing alternatives across multiple criteria. However, traditional normalization techniques often struggle with datasets containing outliers, large variances, or heterogeneous measurement units, which can lead to skewed or biased rankings. To address these challenges, this paper proposes an adaptive, cluster-based normalization approach, demonstrated through a real-world logistics case study involving the selection of a host city for an international event. The method groups alternatives into clusters based on similarities in criterion values and applies logarithmic normalization within each cluster. This localized strategy reduces the influence of outliers and ensures that scaling adjustments reflect the specific characteristics of each group. In the case study—where cities were evaluated based on cost, infrastructure, safety, and accessibility—the cluster-based normalization method yielded more stable and balanced rankings, even in the presence of significant data variability. By reducing the influence of outliers through logarithmic normalization and allowing predefined cluster profiles to reflect expert judgment, the method improves fairness and adaptability. These features strengthen TOPSIS’s ability to deliver accurate, balanced, and context-aware decisions in complex, real-world scenarios.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Multi-Criteria Decision Making · Neural Networks and Applications · Fuzzy Logic and Control Systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

IDMEC, Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisbon, Portugal

Unit for Innovation and Research in Engineering, Polytechnic University of Lisbon, 1959-007 Lisbon, Portugal

Center of Technology and Systems (UNINOVA-CTS), Associated Lab of Intelligent Systems (LASI), 2829-516 Caparica, Portugal

References (31)

Show source-provided references
1. Integrating Multi-Criteria Decision-Making Methods with Sustainable Engineering: A Comprehensive Review of Current Practices10.3390/eng4020088 ↗
2. Hajduk, S., and Jelonek, D. (2021). A Decision-Making Approach Based on TOPSIS Method for Ranking Smart Cities in the Context of Urban Energy. Energies, 14.10.3390/en14092691 ↗
3. Madi, E.N., Zakaria, Z.A., Sambas, A. (2023). Toward Effective Uncertainty Management in Decision-Making Models Based on Type-2 Fuzzy TOPSIS. Mathematics, 11.10.3390/math11163512 ↗
4. Cai, M., and Hong, Y. (2022). Improved TOPSIS Method Considering Fuzziness and Randomness in Multi-Attribute Group Decision Making. Mathematics, 10.10.3390/math10224200 ↗
5. Sałabun, W., Wątróbski, J., and Shekhovtsov, A. (2020). Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods. Symmetry, 12.10.3390/sym12091549 ↗
6. Vakilipour, S., Sadeghi-Niaraki, A., Ghodousi, M., and Choi, S.-M. (2021). Comparison between Multi-Criteria Decision-Making Methods and Evaluating the Quality of Life at Different Spatial Levels. Sustainability, 13.10.3390/su13074067 ↗
7. Qureshi, A.M., and Rachid, A. (2022). Comparative Analysis of Multi-Criteria Decision-Making Techniques for Outdoor Heat Stress Mitigation. Appl. Sci., 12.10.3390/app122312308 ↗
8. Lim, Z.-Y., Ong, L.-Y., and Leow, M.-C. (2021). A Review on Clustering Techniques: Creating Better User Experience for Online Roadshow. Future Internet, 13.10.3390/fi13090233 ↗
9. Krasnov, D., Davis, D., Malott, K., Chen, Y., Shi, X., and Wong, A. (2023). Fuzzy C-Means Clustering: A Review of Applications in Breast Cancer Detection. Entropy, 25.10.3390/e25071021 ↗
10. A Comparison Of K -Means And Fuzzy C -Means Clustering Methods For A Sample Of Gulf Cooperation Council Stock Markets10.1515/foli-2015-0001 ↗
11. Ghadiri, N., Ghaffari, M., and Nikbakht, M.A. (2016). BigFCM: Fast, Precise and Scalable FCM on Hadoop. arXiv.10.1016/j.future.2017.06.010 ↗
12. Chen, Y., and Zhou, S. (2024). Revisiting Possibilistic Fuzzy C-Means Clustering Using the Majorization-Minimization Method. Entropy, 26.10.3390/e26080670 ↗
13. Chan, K.Y., Yiu, K.F.C., Kim, D., and Abu-Siada, A. (2024). Fuzzy Clustering-Based Deep Learning for Short-Term Load Forecasting in Power Grid Systems Using Time-Varying and Time-Invariant Features. Sensors, 24.10.3390/s24051391 ↗
14. Data Normalization Techniques in Decision Making: Case Study with TOPSIS Method10.1504/IJIDS.2018.090667 ↗
15. Comparative Analysis of the Normalization Techniques in the Context of MCDM Problems10.31181/dmame210402001a ↗
16. Comparison of Normalization Techniques on Data Sets with Outliers10.4018/IJDSST.286184 ↗
17. Normalization Techniques for Multi-Criteria Decision Making: Analytical Hierarchy Process Case Study10.1007/978-3-319-31165-4_26 ↗
18. A New Logarithmic Normalization Method in Games Theory10.15388/Informatica.2008.215 ↗
19. A Study of K-Means and C-Means Clustering Algorithms for Intrusion Detection Product Development
20. K-Means Clustering Algorithms: A Comprehensive Review, Variants Analysis, and Advances in the Era of Big Data10.1016/j.ins.2022.11.139 ↗
21. Zolfani, S., Yazdani, M., Pamucar, D., and Zaraté, P. (2020). A VIKOR and TOPSIS Focused Reanalysis of the MADM Methods Based on Logarithmic Normalization. arXiv.
22. Magableh, G.M., and Mistarihi, M.Z. (2024). An Integrated Fuzzy MCDM Method for Assessing Crisis Recovery Strategies in the Supply Chain. Sustainability, 16.10.3390/su16062383 ↗
23. Nabeeh, N.A., Abdel-Basset, M., Gamal, A., and Chang, V. (2022). Evaluation of Production of Digital Twins Based on Blockchain Technology. Electronics, 11.10.3390/electronics11081268 ↗
24. Metalearning-Based Alternating Minimization Algorithm for Nonconvex Optimization10.1109/TNNLS.2022.3165627 ↗
25. A Few-Shot Identification Method for Stochastic Dynamical Systems Based on Residual Multipeaks Adaptive Sampling10.1063/5.0209779 ↗
26. Supervised Kernel Principal Component Analysis for Forecasting10.1016/j.frl.2023.104292 ↗
27. Multisource Information Fusion Considering the Weight of Focal Element’s Beliefs: A Gaussian Kernel Similarity Approach10.1088/1361-6501/ad0e3b ↗
28. Jin, H., Tian, S., Hu, J., Zhu, L., and Zhang, S. (2025). Robust Ratio-Typed Test for Location Change under Strong Mixing Heavy-Tailed Time Series Model. Commun. Stat.-Theory Methods, 1–24.10.1080/03610926.2024.2446396 ↗
29. Robust RGB-T Tracking via Adaptive Modality Weight Correlation Filters and Cross-Modality Learning10.1145/3694686 ↗
30. Adaptive Opinion Dynamics over Community Networks When Agents Cannot Express Opinions Freely10.1016/j.neucom.2024.129123 ↗
31. An Adaptive Agent Decision Model Based on Deep Reinforcement Learning and Autonomous Learning