Large-scale consensus in incomplete social network with non-cooperative behaviors and dimension reduction

Obtaining a consensus solution is a formidable challenge for large-scale decision-making (LSDM) in a social network (SN). The reaching of large-scale consensus in SN is hindered by serious difficulties, including complex decision information, incomplete social relations, a multitude of decision-makers (DMs), and non-cooperative behaviors. This paper introduces a novel three-stage consensus framework that systematically addresses these challenges by data preprocessing, dimension reduction, and optimization modeling. Firstly, the cloud model is applied to convert the probabilistic linguistic information into numerical information, facilitating computational analysis. Meanwhile, an improved t-norm trust propagation method that incorporates the impact of opinion similarity is developed, ensuring the completeness of SN. Secondly, an improved Louvain algorithm is designed to divide large group into cohesive subgroups, enhancing the manageability of LSDM. On this basis, a three-stage consensus optimization that considers non-cooperative behaviors is proposed, which boasts threefold benefits: (i) Assures the synchronous achievement of local and global consensus. (ii) Implements self-adaptive management mechanism of non-cooperative behaviors. (iii) Provides acceptable adjusted opinions for subgroups and DMs. Finally, detailed numerical experiments and comparative analyses are given to demonstrate the effectiveness of the proposed method.