Medical waste risks people and the environment because it can be infectious and contain hazardous substances. For patients to receive medical attention and recover in a safe environment, garbage must be disposed of correctly. Improper medical waste disposal poses a severe risk to society, which can accelerate the development of various pandemics and epidemics. In this case, medical waste disposal should be handled appropriately. This study presents an integrated multi-criteria decision-making method consisting of entropy, PIPRECIA, and MACROS methods based on an interval-valued Fermatean fuzzy set. This method can guarantee high safety and security for health practitioners and society through effective modeling and ranking of risks associated with medical waste disposal. Five alternatives and eight criteria were determined. According to the results, incineration is the most suitable disposal process for healthcare waste. The performance was then assessed and validated using a sensitivity analysis. In addition, the study's findings and their consequences for lawmakers, businesspeople, technologists, and practitioners are examined. In the future, these stakeholders can concentrate on these deficiencies and provide long-term remedies.