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As a consequence of increased awareness of environmental preservation and the associated rigorous regulations, the adoption of sustainable practices has become a crucial element for corporate organizations in regard to their supply chains. In the chemical industry, which is characterized by high risks, high pollution, and high efficiency, these characteristics can help businesses analyze their long-term development and sustainability. The goal of this research is to analyze and choose possible suppliers based on their sustainability performance in the chemical sector. A methodology based on multi-criteria decision making (MCDM) is proposed for this evaluation, using spherical fuzzy analytical hierarchy process (SF-AHP) and combined compromise solution (CoCoSo) methods, in which the novel spherical fuzzy sets theory is employed to present the ambiguous linguistic preferences of experts. In the first stage, an evaluation criteria system is identified through literature review and experts' opinions. The SF-AHP is used to determine the criteria weights, while the CoCoSo method is utilized to select the right sustainable supplier. A case study in the chemical industry in Vietnam is presented to demonstrate the effectiveness of the proposed approach. From the SF-AHP findings, "equipment system and technology capability", "flexibility and reliability", "logistics cost", "green materials and technologies", and "on-time delivery" were ranked as the five most important criteria. From the CoCoSo analysis, Vietnam National Chemical Group (CHE-05) was found to be the best supplier. A sensitivity study and a comparison analysis of methods were also conducted to verify the robustness of the proposed model, and the priority rankings of the best suppliers were very similar. To the best of our knowledge, this is the first study that has proposed SF-AHP and CoCoSo to prioritize SSS evaluation criteria and determine the best alternatives. The suggested method and findings can be used to make well-informed decisions that help businesses to achieve supply chain sustainability, capture opportunities, and maintain competitiveness through reconfiguring resources. The method could be useful for case studies in other countries and for other sustainability problems. [ABSTRACT FROM AUTHOR]