Waste management has come to the fore in the whole world with the increasing impact of the Covid-19 pandemic along with concerns about human health, environmental threats, and socio-economic factors, etc. Medical waste is one of the waste types that need special management processes including particularly collection, storage, separation, and disposal. Healthcare activities create a great amount of medical waste deriving from the hospitals. This study aims to determine the hospital that carries out medical waste management in the most effective way in Erzurum, Turkey. To handle intense uncertainty in the evaluation process, the case is analyzed by Intuitionistic Fuzzy Multi-Criteria Decision-Making (IFMCDM) methods. The present study contributes to the literature by focusing on a real case problem under IF environment in a Group Decision-Making (GDM) framework. Additionally, based on the literature review and expert judgments, the evaluation criteria relevant to the case are defined in this paper. To this end, a four-phased integrated methodology that involves Intuitionistic Fuzzy Weighted Averaging (IFWA), IF Analytical Hierarchy Process (IFAHP), IF Technique for Order Preference by Similarity to Ideal Solution (IFTOPSIS) and One-Dimensional Sensitivity Analysis, is conducted. Firstly, IFWA is aimed to express the significance levels of decision makers (DMs) based on their knowledge, qualifications and experiences. Secondly, IFAHP is used to calculate the importance weights of the decision criteria and IFTOPSIS is preferred to rank the available hospitals. Then, sensitivity analysis is employed to display robustness. According to the results, the most important criteria are Qualified personnel, Health institution infrastructure, and Control of waste, respectively and the most efficient hospital is determined.