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The supplier selection problem (SSP) is known as one of the major issues in the supply chain management area. In this field, the literature shows that the combination of green and agile indicators has been ignored by researchers. Hence, this research attempts to study the SSP considering green and agile aspects, simultaneously. To do this, an efficient hybrid fuzzy decision-making approach is developed based on the Fuzzy Decision-Making Trial and Evaluation Laboratory (FDEMATEL), Fuzzy Best-Worst Method (FBWM), Fuzzy Analytic Network Process (FANP), and Fuzzy Vlse Kriterijumsk Optimizacija Kompromisno Resenje (FVIKOR) methods. Then, to show the efficiency and application of the proposed approach, a case study in the medical devices industry is investigated. After determining the main indicators and alternatives, the interrelationships between indicators are identified employing FDEMATEL. Then, the weights of indicators are calculated using integrated FBWM-FANP. Finally, the potential suppliers are ranked applying FVIKOR. Based on the obtained results, price and greenness are the more important aspects and also material costs, environmental performance evaluation, manufacture flexibility, service level, and system reliability are the most important criteria for the green-agile supplier selection problem in the medical devices industry. Since all of the consistency ratios are less than 0.1, the reliability of the results is proved. On the other side, the results of conducting sensitivity analysis show that by changing the defuzzification methods, there is no significant change in the obtained results that demonstrates the validity of the proposed approach. Eventually, based on the obtained results, suppliers #1 and #5 are the best suppliers for the considered company. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-14690-z.

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