Considering the cognitive, random, uncertain, and flexible constraints, a robust, stochastic, possibilistic, and flexible chance-constrained model was developed based on credibility measurement. The ultimate aim was closedloop supply chain network design. Different attitudes of decision-makers were answered by more flexible measurements of optimistic and pessimistic parameters in the form of credibility measurement. The model has been able to reduce the possible deviation, stochastic deviations, nonfulfillment of demand and capacity constraints, and violation of flexible constraints, which simultaneously include cognitive and random uncertainties and flexibility of constraints in the model. To apply the model, a case study was conducted to design the closed-loop supply chain network of multi-product and multi-period stone paper. The results of implementing the model showed that in different situations and according to the importance of decision makers' opinions, using the range of optimism and pessimism, the number, location of facilities, optimal flow of products and materials between centers in the stone paper supply chain network can be determined. The proposed model was evaluated using robustness and sensitivity analysis, and its performance was evaluated using nominal data in the realization model, which results showed the appropriate performance of the model.