Supplier selection is a crucial multi-criteria decision-making (MCDM) problem which requires a tradeoff between multiple criteria denoting vagueness and imprecision with the involvement of a group of experts. Fuzzy MCDM methods allow for modeling the decision processes involving imprecise and subjective information expressed as linguistic variables or fuzzy numbers by decision-makers. In this paper, considering information fusion between criteria and linguistic terms, a robust supplier selection algorithm based on the hybrid use of a modified fuzzy Analytic Hierarchical Process (FAHP) and generalized Choquet fuzzy integral (GCFI) methods is proposed. The FAHP is employed in order to obtain importance weights of the evaluation criteria and then the GCFI is used to achieve the overall performance values of supplier alternatives. The suggested methodology has been conducted in a real case application for supplier selection problem in a steel-producing company operating in Turkey. We also showed the robustness of the devised methodology through a sensitivity analysis and compared the obtained results with other MCDM methods. Consequently, it is concluded that the proposed integrated approach can effectively handle supplier selection and other MCDM problems especially when there are interdependent sub-criteria in a complex hierarchy of evaluation criteria.