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Due to the high necessity of medical face masks and face shields during the COVID-19 pandemic, healthcare centers dealing with infected patients have faced serious challenges due to the high consumption rate face masks and face shields. In this regard, the supply chain of healthcare centers should put all of their efforts into avoiding any shortages of masks and shields as these products are considered as primary ways to prevent the spread of the virus. Since, any shortages in these products would lead to irrecoverable and costly consequences in terms of the mortality rate of patients and medical staff. Therefore, healthcare centers should decide on best supplier to supply required products, considering technical, and sustainability measures. Dynamicity and uncertainty of the pandemic are other factors that add up to the complexity of the supplier selection problem. Therefore, this paper develops a novel decision-making approach using Measuring attractiveness through a categorical-based evaluation technique (MACBETH) and a new combinative distance-based assessment method to address the supplier selection problem during the COVID-19 pandemic. Due to high uncertainty, vague and incomplete information for decision-making problems during the COVID-19 pandemic, the developed decision-making approach is implemented under fuzzy rough numbers as a superior uncertainty set of the traditional fuzzy set and rough numbers. Extensive sensitivity analysis tests are performed based on parameters of the decision-making approach, impacts of weight coefficients, and consistency of results in comparison to other MCDM methods. A real-life case study is investigated for a hospital in Istanbul, Turkey to show the applicability of the developed approach. Based on the results of MACBETH method, job creation and occupational health and safety systems are two top criteria. Results of the case study for five suppliers indicate that supplier (A1) is the best supplier with a distance score of 3.308. [ABSTRACT FROM AUTHOR]