A cost-minimized two-stage three-way dynamic consensus mechanism for social network-large scale group decision-making: Utilizing K-nearest neighbors for incomplete fuzzy preference relations

In the era of big data, large scale group decision-making (LSGDM) with social networks (SNs) (namely, SN-LSGDM) has become a hot topic in the field of decision science. Faced with the explosive growth of information, decision-makers (DMs) face immense challenges in processing and integrating vast amounts of data, often finding it difficult to fully comprehend all the information, leading to potentially incomplete expressions of their fuzzy preference relations (FPRs). This limitation in information processing not only affects the quality of decision-making but also increases the difficulty and cost of reaching a consensus. To overcome these challenges and enhance the efficiency and accuracy of decision-making, this paper designs a consensus model that minimizes adjustment costs in light of a dynamic trust network. Firstly, we introduce a measurement method based on $K$-nearest neighbor (KNN) information, which comprehensively considers the trust level of DMs and the similarity of preference relations, effectively filling in missing preference information and improving the completeness and accuracy of decision-making. In addition, an improved $k$-means clustering algorithm is adopted, which takes into account the mutual influences between DMs and the cost of unit adjustment. On this basis, a two-stage minimum adjustment cost consensus reaching mechanism based on three-way decision (TWD) is proposed, using comprehensive adjustment priority as the criterion for division, to achieve feedback adjustment at the individual and subgroup levels, ensuring the coordination and consistency of the decision-making plan. At the same time, an optimization model is introduced to achieve cost minimization. Through detailed case studies and comparative analysis, the feasibility and superiority of this method in practical applications have been demonstrated.