Sustainable siting of electric vehicle charging stations via a picture fuzzy divergence-based hybrid multi-criteria model

It remains a major challenge to make reliable decisions in uncertain environments, especially when dealing with imprecise and ambiguous information. Picture fuzzy sets (PFSs), as an extension of traditional fuzzy sets, offer a greater expressive capacity to model uncertainty, neutrality, and refusal. This paper proposes a novel divergence measure, the picture fuzzy arithmetic–geometric divergence (PF-AGD), which overcomes limitations of existing measures for PFSs, such as producing counterintuitive results and undefined values. Building on this measure, we introduce a hybrid decision-making model, called picture fuzzy arithmetic–geometric divergence and closeness coefficient with simple weighted sum product (PF-AGD-CC-WISP), which consists of three key modules: (1) PF-AGD for deriving objective criterion weights; (2) a picture fuzzy closeness coefficient (PF-CC) for capturing subjective decision-maker preferences; and (3) a picture fuzzy weighted sum product method (PF-WISP) to synthesize evaluations and rank the alternatives. To demonstrate the applicability of the proposed model, we apply it to the siting of electric vehicle charging stations, where ten candidate sites are evaluated under twelve economic, technical, environmental, and social criteria. Comparative analysis with existing models shows that the proposed model yields more stable and consistent rankings, highlighting its potential for supporting complex decision-making under uncertainty.