Abstract

In group decision-making with multiplicative reciprocal paired comparison matrices (MRPCMs), existing research uses iterative procedures or optimisation models to improve consistency of individual assessments and build consensus. However, they often create numerous adjustments on original assessments and fail to achieve a comprehensive minimum adjustment cost. Furthermore, the adjustments in the resulting MRPCMs may be not within the predetermined continuous scale. To settle these issues, this article first introduces a logarithmic-distance-based consensus measurement framework. Four-stage sequential goal programming models are then developed to improve consistency of MRPCMs and build consensus with individual consistency control under a continuous or discrete scale. The first stage is to minimise the deviation between original assessments and adjusted ones. The second stage is to minimise the difference between the original priority information and the adjusted priority information. The third stage is to maximise the difference ratio between adjusted assessments and the neutral judgment characterised by ratio 1. The last stage is to minimise the number of modifications on original assessments. Afterwards, the article devises an interactive consistency improving procedure and an interactive group consensus building procedure. Three illustrative examples and comparisons with existing methods are offered to show the usability and efficiency of the developed models.

摘要

在使用乘法互惠配对比较矩阵 (MRPCM) 进行的群体决策中，现有研究使用迭代过程或优化模型来提高个体评估的一致性并建立共识。然而，他们往往会在原有评估基础上进行多次调整，而无法实现综合最低调整成本。此外，生成的 MRPCM 中的调整可能不在预定的连续范围内。为了解决这些问题，本文首先介绍了一个基于对数距离的共识度量框架。然后开发了四阶段顺序目标规划模型，以提高 MRPCM 的一致性，并在连续或离散尺度下与个体一致性控制建立共识。第一阶段是最小化原始评估与调整后评估之间的偏差。第二阶段是最小化原始优先级信息和调整后的优先级信息之间的差异。第三阶段是最大化调整后评估与以比率1为特征的中性判断之间的差异比率。最后阶段是最小化对原始评估的修改次数。之后，文章设计了一个交互式的一致性改进程序和一个交互式的群体共识建立程序。提供了三个说明性示例以及与现有方法的比较，以显示所开发模型的可用性和效率。第三阶段是最大化调整后评估与以比率1为特征的中性判断之间的差异比率。最后阶段是最小化对原始评估的修改次数。之后，文章设计了一个交互式的一致性改进程序和一个交互式的群体共识建立程序。提供了三个说明性示例以及与现有方法的比较，以显示所开发模型的可用性和效率。第三阶段是最大化调整后评估与以比率1为特征的中性判断之间的差异比率。最后阶段是最小化对原始评估的修改次数。之后，文章设计了一个交互式的一致性改进程序和一个交互式的群体共识建立程序。提供了三个说明性示例以及与现有方法的比较，以显示所开发模型的可用性和效率。