Multi-attribute decision-making (MADM) relies heavily on the aggregation of fuzzy data, yet determining the most appropriate decision remains challenging, especially when information is limited or uncertain. To address this, recent research has introduced Aczel-Alsina (AA) aggregation operators (AOs) for different types of fuzzy sets. This study proposes novel Fermatean fuzzy aggregation operators by incorporating AA t-norm and AA t-conorm, along with the development of AA product and AA sum for Fermatean fuzzy sets. Additionally, we introduce two innovative operators: the Fermatean fuzzy AA weighted averaging and Fermatean fuzzy AA weighted geometric operators. The theoretical properties of these operators, including idempotency, monotonicity, and boundedness, are rigorously analyzed. To validate the effectiveness of the proposed approach, we apply it to a decision-making problem in the cross-border e-commerce environment, focusing on AI-driven consumer behavior prediction and personalized targeted advertising campaigns. A global retail firm utilizing AI algorithms to analyze large-scale consumer data is examined as a case study. Our method enhances decision-making by aligning marketing strategies with cultural and consumption patterns across different regions, ultimately improving customer engagement and increasing sales. Comparative analysis with existing methodologies demonstrates that our approach outperforms conventional techniques, offering a more accurate and adaptable decision-making framework. This research contributes to the broader understanding of AI-based personalization in business environments. It reinforces its role as a robust decision-support tool for sustainable and socially responsible global market interactions.