The recent advances in sustainable supply chain management are integrated with Industry 4.0 concepts. This study develops a new integrated model to consider the sustainability and Industry 4.0 criteria for the supplier selection management. The proposed approach consists of the fuzzy best worst method (FBWM) and the two-stage fuzzy inference system (FIS) to assess the selection of suppliers. Firstly, this study determines a comprehensive list of Industry 4.0 and sustainability criteria along with their definitions. Then, the importance weight of each criterion is computed by the FBWM. Subsequently, a two-stage FIS is devoted to nominate the suppliers' performance with regard to the sustainability and Industry 4.0 criteria. To show the applicability of our integrated model, a case study for a textile company in Iran is provided. Finally, some sensitivity analyses are done to assess the efficiency of the proposed integrated approach. One finding is to establish a decision-making framework to evaluate suppliers separately, rather than relatively in a fuzzy environment using Industry 4.0 and sustainability criteria.