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This paper presents a new hybrid decision-making support method (New Hesitant Fuzzy AHP-QFD-PROMETHEE II Method), which jointly uses the Analytic Hierarchy Process (AHP), the Quality Function Deployment (QFD) and the Preference Ranking Method for Enrichment Evaluation (PROMETHEE II), as well as the Hesitant Fuzzy Linguistic Term Sets (HFLTS) to capture hesitation and aggregate divergent opinions from different experts. A real application of the new method to a packaging design selection problem for an automotive company is described, finding that AHP assisted in determining the importance of QFD's customer requirements (CRs) and PROMETHEE II was used to select the best packaging design. With this same problem, for the purpose of validating the proposed method, a comparative analysis was made with the use of the Hesitant Fuzzy AHP-QFD-TOPSIS method and also with the traditional AHP-QFD-PROMETHEE method, which makes it impossible to capture the hesitation of decision makers. The result showed similarity in the rankings of design alternatives found in the three methods application. The proposed method proved advantageous for solving problems that can generally be solved with the QFD House of Quality but have serious difficulties when decision makers have divergent opinions and hesitate in evaluating criteria and alternatives. [ABSTRACT FROM AUTHOR]