# Adaptive Cluster-Based Normalization for Robust TOPSIS in Multicriteria Decision-Making
## 2 Literature Review
Unlike traditional clustering algorithms, which are often accessible through built-in software tools with minimal coding, FCM and similar approaches demand manual parameter tuning (e.g., selecting the optimal fuzziness coefficient m) and careful data preprocessing to produce meaningful results [11]. Additionally, FCM is highly sensitive to initialization--poorly selected initial centroids can lead to suboptimal clustering outcomes, often requiring advanced techniques such as genetic algorithms or particle swarm optimization to enhance results. Consequently, while fuzzy clustering offers improved accuracy and flexibility, its practical application demands greater expertise, computational resources, and algorithmic fine-tuning [12]. Recent research has focused on reducing the computational overhead associated with fuzzy clustering by exploring hybrid models that combine deep learning and optimization algorithms. These models aim to automate parameter selection and improve overall performance. Such advances seek to make fuzzy clustering more accessible and scalable, bridging the gap between its theoretical strengths and practical usability in complex, real-world decision-making scenarios [13]. Normalization is a critical step in multi-criteria decision-making (MCDM) processes, as it ensures that criteria measured on different scales can be compared meaningfully [14]. Common normalization methods include Min-Max normalization: This method rescales data to a fixed range, typically [0, 1], but is sensitive to outliers, which can distort the normalized values. Z-Score normalization: This technique standardizes data based on mean and standard deviation, assuming a normal distribution, which may not hold true for all datasets. Vector normalization: Often used in TOPSIS, this method normalizes data by dividing each criterion value by the Euclidean norm of the vector. While effective, it may not always preserve proportional differences between criteria. These conventional normalization techniques face challenges when applied to highly skewed data, extreme values, or non-linear distributions, which can compromise the fairness and accuracy of decision-making outcomes. For example, the choice of normalization method can significantly influence the ranking of alternatives in MCDM processes, underscoring the importance of selecting an appropriate technique for each specific decision context [15; 16]. Logarithmic transformation is a mathematical technique used to handle non-linear data and compress large numerical ranges. By applying a logarithmic function, data can be transformed to reduce skewness, manage outliers, and stabilize variance. This transformation preserves relative differences while minimizing the influence of extreme values, making it useful in fields such as statistics, finance, and machine learning. Despite these advantages, logarithmic normalization remains underutilized in MCDM methods like TOPSIS. Integrating it into the TOPSIS framework could improve ranking stability and decision accuracy--especially in datasets characterized by high variance [17]. One study introduced a novel logarithmic normalization method within the context of game theory, demonstrating its effectiveness in separating normalized values more efficiently than conventional approaches. These findings suggest promising applications for such a method in MCDM frameworks as well [18]. The current literature reveals a lack of studies that combine fuzzy clustering with centroid-based distance allocation within MCDM frameworks [19; 20]. Furthermore, although logarithmic normalization offers clear advantages for handling high-variance data, its application within TOPSIS and other MCDM models remains limited [21]. Addressing these gaps presents an opportunity to improve decision-making processes by developing a unified framework that integrates both techniques, thereby enhancing clustering precision and ranking accuracy within MCDM applications [22].