Multi-dimensional multi-round minimum cost consensus models with iterative mechanisms involving reward and punishment measures

Abstract

In order to address the issues of unfairness in consensus and subjectivity bias in data, while further expanding the traditional minimum cost consensus model (MCCM) in terms of opinion dimension and consensus round, we propose the multi-dimensional MCCM (MD-MCCM) and multi-round MCCM (MR-MCCM). Subsequently, we introduce the concepts and definitions pertaining to these two variants of consensus and formulate their respective consensus model frameworks. To benefit from the advantages of both, we integrate these two types of consensus models, thereby introducing the concept of multi-dimensional multi-round minimum cost consensus. To address the issues of unfairness and subjectivity in the consensus-reaching process, we propose two specific reward and punishment measures and devise the multi-dimensional multi-round consensus iterative mechanisms. These mechanisms facilitate an iterative update of decision-makers’ opinions, weights, and unit costs within the feedback process. Based on this foundation, we construct the multi-dimensional multi-round MCCM (MDMR-MCCM) involving Euclidean and Manhattan distance measures, and their corresponding algorithm and consensus reaching process are presented. Finally, a group decision problem concerning site selection validates the rationality and effectiveness of our models. Moreover, a comparative analysis of results obtained using different models is provided.