In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible. In this paper, we focus on the decision- making problem by a projection model (Algorithm I) whose attribute values are given in the forms of dual hesitant fuzzy elements (DHFEs). In order to reflect the information of the data more accurately, we first divide the dual hesitant fuzzy decision matrix into membership degree matrix and non-membership degree matrix. Then we gain the virtual positive ideal solution from the membership degree matrix and the negative positive ideal solution from the non-membership degree matrix. And then the projection values from every solution to the virtual positive ideal solution and the negative positive ideal solution are calculated. In combination with the two projection values, the relative consistent degree is further calculated to rank all the alternatives. At the same time, in order to guarantee the rationality of the decision-making result, a variation coefficient method is developed to determine the weights of the attributes under dual hesitant fuzzy environment objectively. Finally, the existing algorithms (Algorithm II and Algorithm III, Algorithm IV, Algorithm V) are compared with our algorithm (Algorithm I). The comparison result shows that Algorithm I is a valuable tool for decision making.

在决策过程中，保留原始数据信息成为最关键的一步。双重犹豫模糊集（DHFS）可以反映DMs给出的原始隶属度和非隶属度信息，是DMs尽可能提供原始信息的一种新工具。在本文中，我们通过投影模型（算法 I）关注决策问题，其属性值以对偶犹豫模糊元素（DHFE）的形式给出。为了更准确地反映数据的信息，我们首先将双犹豫模糊决策矩阵划分为隶属度矩阵和非隶属度矩阵。然后我们从隶属度矩阵中得到虚正理想解，从非隶属度矩阵中得到负正理想解。然后计算每个解到虚正理想解和负正理想解的投影值。结合两个投影值，进一步计算相对一致度，对所有备选方案进行排序。同时，为了保证决策结果的合理性，提出了变异系数法，客观地确定了双重犹豫模糊环境下属性的权重。最后，将现有算法（算法 II 和算法 III、算法 IV、算法 V）与我们的算法（算法 I）进行比较。比较结果表明，算法 I 是一种有价值的决策工具。