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The present paper deals with an integrated sustainable supply chain model with the effect of learning for an imperfect production system under a cloudy fuzzy environment where the demand rate is treated as a cloudy triangular fuzzy (imprecise) number, which means that the demand rate of the items is not constant, and shortages and a warranty policy are allowed. The vendor governs the manufacturing process to serve the demand of the buyer. When the vendor supplies the demanded lot after the production of items, it is also considered that the delivery lots have some defective items that follow an S-shape learning curve. After receiving the lot, the buyer inspects the whole lot, and the buyer classifies the whole lot into two categories: one is the defective-quality items and the other is the imperfect-quality items. The buyer returns the defective-quality items to the seller after a screening process, for which a warranty cost is included. During the transportation of the items, a lot of carbon units are emitted from the transportation, damaging the quality of the environment. The seller includes carbon emission costs to achieve sustainability as per considerations. A one-time discrete investment is also included for the minimizing of the setup cost of the seller for the next cycles. We developed models for the scenario of the separate decision and for the integrated decision of the players (seller/buyer) under the model’s consideration. Our aim is to jointly optimize the integrated total fuzzy cost under a cloudy fuzzy environment sustained by the seller and buyer. Numerical examples, sensitivity, analysis limitations, future scope and conclusions have been provided for the justification of the proposed model, and the impact of the input parameters on the decision variables and integrated total fuzzy cost for the supply chain are provided for the validity and robustness of this proposed model. The effect of learning in a cloudy fuzzy environment was positive for this proposed model. Full article