Cloud computing has emerged as a transformative technology in the healthcare industry, but selecting the most suitable CV (“cloud vendor”) remains a complex task. This research presents a decision framework for CV selection in the healthcare industry, addressing the challenges of uncertainty, expert hesitation, and conflicting criteria. The proposed framework incorporates FFS (“Fermatean fuzzy set”) to handle uncertainty and data representation effectively. The importance of experts is attained via the variance approach, which considers hesitation and variability. Furthermore, the framework addresses the issue of extreme value hesitancy in criteria through the LOPCOW (“logarithmic percentage change-driven objective weighting”) method, which ensures a balanced and accurate assessment of criterion importance. Personalized grading of CVs is done via the ranking algorithm that considers the formulation of CoCoSo (“combined compromise solution”) with rank fusion, providing a compromise solution that balances conflicting criteria. By integrating these techniques, the proposed framework aims to enhance the rationale and reduce human intervention in CV selection for the healthcare industry. Also, valuable insights are gained from the framework for making informed decisions when selecting CVs for efficient data management and process implementation. A case example from Tamil Nadu is presented to testify to the applicability, while sensitivity and comparison analyses reveal the pros and cons of the framework.