This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of interval-valued dual hesitant fuzzy elements (IVDHFEs) and the attribute weights are unknown. Firstly, motivated by the distance definitions of the hesitant fuzzy elements and dual hesitant fuzzy elements, the distance definitions of the interval-valued dual hesitant fuzzy elements are proposed. Then, the grey relational projection method based on the distance measure between the interval-valued dual hesitant fuzzy elements is proposed. To get the attribute weights, the nonlinear optimization model with the minimum total deviation of the grey relational coefficient is constructed. Furthermore, a novel interval-valued dual hesitant fuzzy MADM method is proposed based on the grey relational projection. Finally, a numerical example is given to demonstrate the effectiveness and practicality of the developed method.
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