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An appropriate and sustainable waste management plan is required in different scenarios for global development. The main goal of this paper is to evaluate a waste management problem by investigating an integrated multi-objective environment through solid transportation problem. To develop sustainability, three objective functions are optimized by choosing as cost for economical opportunity, time for social satisfaction and carbon emission for environmental view. Cap and trade policy is regarded here to minimize carbon emission and to provide some economical opportunities to the system. To control hesitancy of this scenario, twofold uncertainty (type-2 intuitionistic fuzzy) is incorporated here, and this uncertainty is defuzzified by a ranking operator. A strategy is proposed here to optimize three factors of sustainability by an intellectual model formulation of solid waste management. To check the appropriateness of the proposed model, two numerical problems are evaluated using two advanced methods, namely, neutrosophic linear programming and ϵ -constraint method. The Pareto-optimal solutions are derived by the variation of cap value and fulfilling the criteria of sustainability. The obtained results indicate that cap and trade policy or waste management, or both are highly sophisticated for applying in real-world application. The overall conclusions recommend that a government or NGO should encourage transportation system, or the industry to minimize carbon emission by utilizing several carbon policies. It can assist to establish different new project of waste management in a discrete environment, based on sustainability. [ABSTRACT FROM AUTHOR]