关键词: 调和概率, 共识达成, 聚类, 最小成本

Abstract: Group decision-making effectively leverages the wisdom of decision-makers with different knowledge structures and experiences to improve decision performance. It is an effective approach to solving complex decision problems. In particular, in large-scale group decision-making involving decision-makers from different fields, when there are significant differences in individual decision information, an adjustment mechanism will be activated. In such cases, certain decision-makers may need to modify their initial judgments. Based on this, this paper proposes a three-stage adjustment model based on linguistic subscript value modification, aiming to address the challenge of adjusting individual decision-maker evaluations in the process of achieving consensus in probabilistic linguistic group decision-making.
To achieve group consensus more efficiently, the use of large group decision-making techniques can improve decision performance. Among them, K-means clustering can significantly improve the decision efficiency of large groups and has attracted the attention of scholars. However, due to the influence of the number of clusters and clustering models, there is a considerable error in the clustering results, so it is necessary to determine the optimal number of clusters to improve the clustering effect of large groups. Through this process, we can obtain more accurate classification results, thereby better understanding the contribution of individual opinions to group consensus.
In terms of individual opinion adjustment, traditional feedback processes only focus on the consensus level of a single aspect, and consensus is achieved through methods such as forcing decision-makers to modify their opinions, resulting in decision results deviating from the original viewpoints of individual decision-makers. These practices make a relatively weak analysis of the impact mechanism of individual adjustment results on group aggregation, so it is necessary to further identify the decision-makers and adjustment directions that need to be adjusted effectively. Therefore, in order to improve the adjustment efficiency in a probabilistic linguistic environment, this paper fully considers the individual acceptance of decision-makers and the premise of group cohesion, and designs a three-stage feedback adjustment model based on linguistic subscript values.
Next, we design a group consensus measurement model from four dimensions. Through this model, we can identify the linguistic subscript values of subgroups and individual decision-makers that need adjustment. In this way, we can target these groups and individuals for evaluation and adjustment, improving the effectiveness of group consensus implementation. To achieve the principle of minimum cost, we propose a three-stage feedback adjustment mechanism based on linguistic subscript values. With this mechanism, we can dynamically make an adjustment based on the evaluation values of individual decision-makers to better meet the requirements of group consensus. In this way, while ensuring the effectiveness of adjustments, we can minimize the cost of adjustment.
Finally, we illustrate the superiority and application value of our method through a case study of green supplier evaluation. This case demonstrates the effectiveness of our method in practical problems and indicates its wide applicability in different decision-making fields.
In conclusion, the consensus implementation process framework designed in this paper is based on the principle of minimum adjustment cost. By analyzing influencing mechanisms, designing measurement models, and proposing feedback adjustment mechanisms, it effectively addresses the challenge of adjusting individual decision-maker evaluations. The framework has demonstrated superiority and practical value, providing a feasible solution for achieving group consensus. In the future, we will consider improving the clustering constraint from the perspective of coordination cost. The knowledge graph is established based on the background of experts, and the reachable relationship among experts is deeply explored.

Key words: harmonic probability, consensus reaching process, clustering, minimum cost