In this paper, we propose two-stage prioritization procedure (TSPP) for multiplicative Analytic Hierarchy Process-group decision making (AHP-GDM), which involves determining the group priority vector based on the individual pair-wise comparison matrices (PCMs), simultaneously considering the consensus and consistency of the individual PCMs. The first stage of the TSPP involves checking and revising the individual PCMs for reaching the acceptable consensus and consistency. The second stage of the TSPP involves estimating the group priority vector using Bayesian approach. The main characteristics of the proposed TSPP are as follows: 1) It makes full use of the prior information as well as the sample information during the Bayesian revision of the individual PCMs and the Bayesian estimation of the group priority vector; 2) It ensures that the revised individual PCMs reach the acceptable consensus and consistency; 3) It enriches the aggregation methods for the collective preference in multiplicative AHP-GDM. Finally, two numerical examples are used to evaluate the applicability and effectiveness of the proposed TSPP by the comparisons with several other methods.

中文翻译：

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乘法 AHP 组决策的两阶段优先级排序程序

在本文中，我们提出了用于乘法层次分析过程组决策 (AHP-GDM) 的两阶段优先级程序 (TSPP)，它涉及基于单个成对比较矩阵 (PCM) 同时确定组优先级向量考虑到各个 PCM 的共识和一致性。TSPP 的第一阶段涉及检查和修订各个 PCM，以达到可接受的共识和一致性。TSPP 的第二阶段涉及使用贝叶斯方法估计组优先级向量。所提出的TSPP的主要特点如下：1）充分利用了个体PCM的贝叶斯修正和组优先向量的贝叶斯估计过程中的先验信息和样本信息；2）保证修改后的单个PCMs达到可接受的共识和一致性；3）丰富了乘法AHP-GDM中集体偏好的聚合方法。最后，通过与其他几种方法的比较，使用两个数值例子来评估所提出的 TSPP 的适用性和有效性。