Uncertainty-Aware Fuzzy Centrality Measures for Influential Node Identification: A Structural Modeling Approach Toward E-Commerce Applications

In recent years, e-commerce platforms have become one of the most prominent examples of large-scale interaction networks, where understanding influence dynamics among users, products, and digital entities is essential for applications such as online marketing, recommendation systems, and customer behavior analysis. A key challenge in these platforms is that interactions are often uncertain, noisy, and inferred from implicit signals rather than explicitly defined relationships. This uncertainty cannot be effectively captured using deterministic network models. To address this issue, this paper proposes an uncertainty-aware centrality framework for identifying influential entities in e-commerce interaction networks modeled as fuzzy graphs. Unlike existing fuzzy centrality measures that produce single crisp values, the proposed method assigns a fuzzy degree set to each node, preserving multiple possible influence levels along with their associated membership values. Max-min decomposition is employed to enable principled fuzzy inference and accurate uncertainty propagation. Furthermore, a novel ranking strategy is introduced that determines node rankings directly from fuzzy sets without requiring pairwise comparisons, thereby significantly reducing computational complexity. The proposed framework is evaluated on multiple real-world benchmark networks with fuzzy edge annotations, which are widely used as structural proxies for complex interaction systems. Extensive experimental results demonstrate that the proposed method outperforms state-of-theart centrality measures in terms of ranking accuracy, robustness, and computational efficiency. These findings highlight the effectiveness of the proposed approach as a general methodological tool for influence analysis in e-commerce systems under uncertainty.