Businesses establish supply chains in order to continue their activities. Choosing the suppliers to take part in these supply chains poses many challenges in rapidly changing conditions. Environmental concerns in the public, competitive market structures, and developing technological opportunities affect the decision-making processes. Different criteria are taken into consideration instead of traditional criteria such as cost and service. In this study, green, agile, and Industry 4.0 dimensions and the criteria under these dimensions are defined. According to these, the problem of selecting the supplier that responds to the expectations of the markets and enables them to increase their competitiveness was discussed. Fuzzy SWARA and fuzzy BMW methods were applied in an integrated way to solve the supplier selection problem under these three dimensions. A real case study was also presented. In the study, the results obtained by creating different scenarios were compared and sensitivity analysis was made. The results obtained show that the hybrid method developed in this study is effective in supplier selection problems. As a result of the study, the most important evaluation dimension is "agile" and the most important criterion is "delivery speed".