# Adaptive Cluster-Based Normalization for Robust TOPSIS in Multicriteria Decision-Making
## 6 Conclusions  
This study introduced two methodological innovations to enhance the TOPSIS decision-making framework: Clustering Using Fuzzy Numbers and Centroid-Based Distance Allocation and logarithmic normalization. Together, these methods address key limitations in traditional MCDM approaches, particularly in the handling of uncertainty, outliers, and rigid data-driven classifications. The proposed clustering approach allows decision-makers to define ideal cluster profiles independently of the dataset, enabling greater strategic control. Fuzzy numbers are used exclusively to model uncertainty in the evaluation of alternatives, which are then converted to crisp values to calculate Euclidean distances from predefined centroids. This results in a robust yet transparent classification method, free from iterative optimization or probabilistic membership functions. Unlike traditional clustering techniques such as K-Means, which derive centroids from data, our approach decouples clustering from data distribution and focuses on alignment with idealized profiles--offering greater interpretability and consistency. Logarithmic normalization further enhances the robustness of the TOPSIS method by smoothing extreme values and preserving proportional differences across criteria. This is es pecially useful in datasets with high variance or non-linear distributions, where traditional normalization techniques may distort rankings. The case study results demonstrate that the proposed methodologies significantly enhance both the accuracy and stability of decision-making outcomes. The fuzzy clustering approach enables more realistic classification of alternatives, while logarithmic normalization improves the comparability of criteria--without adding unnecessary complexity. A key advantage of both methods is their computational simplicity and ease of implementation, making them accessible for a broad range of practical applications. Beyond the context of city selection, the proposed methodology offers broader enhancements to decision-making by improving how alternatives are grouped and compared in the presence of uncertainty and variability. Its modular design--combining fuzzy-based evaluation, predefined cluster centroids, and adaptive normalization--makes it suitable for various domains such as supply chain optimization, financial assessment, environmental planning, and strategic project prioritization. The method supports more robust, context-aware, and scalable decision processes across diverse real-world applications. Although the results are promising, there remain several opportunities for further exploration and validation. A logical next step is to test the performance of these techniques within other MCDM models--such as VIKOR, PROMETHEE, and AHP--to assess their adaptability across different decision-making frameworks. Each of these models has unique characteristics, and applying the proposed methods within them could offer deeper insights into their generalizability and effectiveness. Despite its promising results, the proposed methodology presents some limitations. The definition of ideal cluster centroids is currently based on expert judgment, which, while offering flexibility and interpretability, may introduce a degree of subjectivity. Future refinements could explore hybrid or data-assisted strategies to support or validate these predefined profiles. Additionally, while the method is computationally simple and effective in the case study, its performance in large-scale or high-dimensional problems remains to be tested. Moreover, although the proposed approach was applied within the TOPSIS framework, evaluating its integration with other MCDM models (e.g., VIKOR, PROMETHEE, AHP) would help assess its generalizability. Finally, future work could involve benchmarking the proposed methods against other clustering and normalization techniques.