Navigating Cross-Border E-Commerce: Prioritizing Logistics Partners with Hybrid MCGDM

As global e-commerce expands, efficient cross-border logistics services have become essential. To support the evaluation of logistics service providers (LSPs), we propose HD-CBDTOPSIS (Technique for Order Preference by Similarity to Ideal Solution with heterogeneous data and cloud Bhattacharyya distance), a hybrid multi-criteria group decision-making (MCGDM) model designed to handle complex, uncertain data. Our criteria system integrates traditional supplier evaluation with cross-border e-commerce characteristics, using heterogeneous data types-including exact numbers, intervals, digital datasets, multi-granularity linguistic terms, and linguistic expressions. These are unified using normal cloud models (NCMs), ensuring uncertainty is consistently represented. A novel algorithm, improved multi-step backward cloud transformation with sampling replacement (IMBCT-SR), is developed for converting dataset-type indicators into cloud models. We also introduce a new similarity measure, the Cloud Bhattacharyya Distance (CBD), which shows superior discrimination ability compared to traditional distances. Using the coefficient of variation (CV) based on CBD, we objectively determine criteria weights. A cloud-based TOPSIS approach is then applied to rank alternative LSPs, with all variables modeled using NCMs to ensure consistent uncertainty representation. An application case and comparative experiments demonstrate that HD-CBDTOPSIS is an effective, flexible, and robust tool for evaluating cross-border LSPs under uncertain and multi-dimensional conditions.