Healthcare networks are sophisticated systems, which are commonly comprised of medical and drug suppliers, insurance companies, third-party logistics (3PL) providers, and regulators. Effective healthcare systems should be capable of sustainably delivering high quality and accessible patient care services using data shared through the best available technologies. However, healthcare data are generally hard to comprehend, use, and share since they are also inaccessible, non-standardized, and disseminated throughout the network. Blockchain may be employed to alleviate the impact of these challenges. However, only a few blockchain platforms (BP) have reached the stable design and established user base needed to give a healthcare organization (HO) confidence in their implementation. Each digital transformation project employing blockchain faces the challenge of picking a BP suitable to the requirements of a HO. While some research has been conducted to choose an appropriate BP, quantitative studies on specific industries, including healthcare, are currently insufficient. This investigation provides a case addressing the selection of the most feasible BP for a healthcare group. To this end, we propose a new multi-criteria decision-making (MCDM) framework that integrates the extent analysis-based rough Analytic Hierarchy Process (RAHP-E) and rough Compromise Programming (RCP). The findings of this study are validated through several analyses.