Clustering analysis is a key technique in reducing the dimensionality of high volume irregular data containing large-scale group decision-making (LSGDM) information. Uncertainty theory is suitable for subjective estimation or situation, such as lack of historical data, and it can be employed to effectively express the uncertainty of trust and preference information in LSGDM problems. This paper studies the dimensionality reduction and subgroup optimization in LSGDM by utilizing linear uncertain variables in social networks. A clustering method is proposed to decompose the large group into several subgroups of higher consilience degrees and higher preference similarities, and lower the dimension of information for LSGDM. In the clustering process, two measurement attributes, trust relationship and preference relationship of decision-makers, are combined, and information consistent degree is utilized as the clustering indicator. This approach does not need to preset the threshold and the number of subgroups, and can be employed to obtain subgroups with similar preferences and stable trust relationship. Through the clustering reliability evaluation of subgroups, the rationality of large-scale group clustering results is verified. Subgroup consensus contribution is used to identify superior subgroups and quantify the role of subgroups in improving the consensus level. An example of emergency decision-making and comparative analysis is provided to explain the feasibility and advantages of the proposed method.

The social network group decision-making is popular due to the advantages of social relationships in the consensus reaching process, especially the trust relationships. To explore the effects of trust on consensus, some minimum cost consensus models are proposed based on implicit trust between individuals and the moderator. The implicit trust is computed based on the similarity of opinions and it is implied into the traditional minimum cost consensus model to obtain a new quadratic programming problem and the related dual problem. The weights of individuals can be determined based on implicit trust and can be used to modify the possible deviations among individuals’ adjustment costs. A numerical example and the comparative analysis are given to analyze the effectiveness of the proposed models, which suggests that individuals are willing to give up some benefit to reach consensus due to their implicit trust to the moderator and make minor revisions to their adjustment costs due to their implicit trust to each other.