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• Offering a novel fuzzy robust approach for closed-loop supply chain network design. • Examining the hybrid uncertainties and flexibility of constraints in the problem. • Considering economic, responsibility, and environmental subjects in modeling. • Using the interactive fuzzy programming approach to solve the multi-objective model. • Introducing a new application for stone paper closed-loop supply chain network design. Nowadays, the production of stone paper, in addition to its widespread utilization in various fields, does not require water consumption, cutting down trees, and stone paper products are easily recyclable and recoverable. Due to the importance of developing and using stone paper and paying attention to environmental matters, Closed-Loop Supply Chain Network Design (CLSCND) is very important for stone paper products. Moreover, due to epistemic, randomness uncertainties, the uncertainties in Objective Function (OF), and the flexible constraints for CLSCND in the real world, this paper introduces a novel Mixed Robust Stochastic, Possibilistic, and Flexible Programming (MRSPFP) approach based on credibility theory. The different attitudes of the Decision-Makers (DMs) are addressed by a more flexible measurement of the optimistic and pessimistic parameters using the criterion of credibility. In the study, a comprehensive procedure is proposed for stone paper CLSCND, to minimize costs, increase responsiveness by minimizing transit time between different facilities, and regarding environmental concerns into account through minimizing carbon emissions. The model is solved utilizing an interactive fuzzy programming solution procedure and the Best-Worst Method (BWM). The results of sensitivity analysis, the effect of changing the problem parameters, and the performance of the proposed model are investigated and compared. The results show that the MRSPFP model has a better performance compared to other previous models. The MRSPFP model performs better in strategic decisions that require high investment costs due to the minimization of the absolute deviation of OF from its mean. Also, the applied results of the study show that CLSCND has a good capability and potential for sustainable development in the field of stone paper. [ABSTRACT FROM AUTHOR]