This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables, called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to represent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency- based interactive algorithm to derive multiplicative linguistic intuitionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to calculate the agreement degree of DMLPRs and build an optimal model to increase the consensus level of individual DMLPRs. Finally, a new GDM method (call Algorithm III) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environments of DMLPRs.

本文基于对偶乘法语言偏好关系（DMLPRs）的一致性和一致性分析，提出了一种新的群决策（GDM）方法。提出了一种新类型的语言变量，称为双重乘法语言变量 (DMLV)，它是在乘法语言尺度上定义的。DMLV 用于表示决策者 (DM) 的非对称定性犹豫判断。提出了一种基于最大一致性的交互式算法，用于推导乘法语言直觉偏好关系（MLIPR），由此获得了 DMLPR 的一致性概念。然后，我们定义了不一致 DMLPR 的概念，并提出了一种基于最优模型的方法来推导一致 DMLPR。此外，不完整的 DMLPR 也可以通过提出的基于最大一致性的交互算法来处理。对于 GDM，DM 的权重由各个 DMLPR 之间的基于余弦的相关系数决定。此外，我们提出了一种共识措施来计算 DMLPRs 的一致程度，并构建一个最优模型来提高单个 DMLPRs 的共识水平。最后，一种新的 GDM 方法（调用提供了算法 III ) 并使用一个应用示例来说明所提出的 GDM 方法。所提出的 GDM 方法在 DMLPR 环境中优于以前的 GDM 方法。