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In Vietnam, as more and more organizations are moving toward globalization, green supplier selection (GSS) has emerged as a strategic approach in supply chain management that requires supplier practices in lessening the environmental risks to society. Based on both conventional and environmental criteria, this paper aims to evaluate a set of suppliers by establishing a multi-criteria decision-making (MCDM)-based framework using an integrated fuzzy analytical hierarchy process (FAHP) with the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Initially, five GSS criteria of the environmental aspect (wastewater treatment, solid waste generation, energy consumption, air pollution, corporate social responsibility) and conventional criteria (quality, cost, delivery, and technology) are identified from the literature and consulting field experts to employ the MCDM approach. The trustworthiness of the proposed integrated framework is presented by discussing a case study in the coffee bean supply chain in Vietnam. The FAHP is used to generate criteria weights in which fuzzy set theory is applied to translate the linguistic evaluation statements of experts, and VIKOR is used to rank the alternatives against the selected criteria. From FAHP findings, the most important criteria are quantity discount, solid waste generation, order fulfillment rate, logistics cost, and purchasing cost. A consistency test is performed to ensure the uniformity of the expert’s input. The best suppliers are determined through the final ranking of the VIKOR model for the case study. The work presented provides insight to decision-makers of supplier selection that helps determine significant GSS criteria and aids in the minimization of environmental risks to society arising from the supply chain on corporate sustainability standards.