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Closed-loop supply chain is a prominent strategy that effectively alleviates the environmental burden on natural resources within the circular economy framework. Notwithstanding the conventional closed-loop supply chain models, this study addresses a conflicting bi-objective four-echelon model with a sole supplier, manufacturer, retailer, and collector subject to carbon emission controlling strategies for each and every chain partner under fuzzy environment. This study maximizes the overall profitability of the centralized model, whereas a second objective aims at boosting its proportion of product output limiting carbon emissions. This study enhances the well-established min-max method based interactive fuzzy bi-objective optimization algorithm by incorporating the absolute difference function along with the trade-off ratio based autonomized optimization approach. By using two different sets of autonomized desired levels, the proposed algorithm yields a preferred Pareto optimal solution to the fuzzy stochastic bi-objective non-linear programming model. To enhance profitability sustainably, this study pleads managers to put more thrust on governing the manufacturer’s buy-back expenses while improving the consumer demand for freshly produced items. Nevertheless, the demand for newly manufactured goods and the expenses associated with buying back product from the collector marginally increase the overall product production, imposing limitations on carbon emissions.