Social networks (SNs) have become popular as a medium for disseminating information and connecting like-minded people. They play a central role in decision-making by correlating the behaviors and preferences of connected agents. However, it is difficult to identify social influence effects in decision-making. In this article, we propose a framework of how to describe the uncertain nature of the social network group decision-making (SN-GDM) process. Social networks analysis (SNA) and quantum probability theory (QPT) are combined to construct a decision framework considering superposition and interference effects in SN-GDM scenarios. For the first time, we divide interference effects into symmetry and asymmetry. We construct an influence diagram, which is a quantum-like Bayesian network (QLBN), to model group decisions with interactions. We identify symmetry interference terms from Shapley value and asymmetry interference terms from trust value, respectively. The probability of an alternative is calculated through quantum probability theory in our influence diagram. The combination of QLBN model and social network could gain an understanding of how the group preferences evolve within SN-GDM scenarios, and provide new insights into SNA. Finally, an overall comparative analysis is performed with traditional SNA and other quantum decision models.

Quantum decision theory has been successfully applied to multi-attribute group decision-making (MAGDM) to model decision-makers’ interference and superposition effects in recent years. Existing quantum models assume that interference effects among decision-makers are symmetric. However, asymmetric interference effects have been ignored. We propose a VIKOR-based linguistic distribution assessments (LDAs) model considering asymmetric interference effects in a quantum decision scenario. Firstly, we combine VIKOR with LDAs to obtain a compromise solution in a fuzzy multi-attribute decision scenario with conflicting attributes. Secondly, an aggregation framework based on quantum probability theory is constructed to explore group preferences considering asymmetric interference effects among decision-makers. Finally, the model is compared with other methods to confirm its validity and stability.

Virtual power plants (VPPs) offer an effective means to address the imbalance issue between electricity supply and demand to advance the world’s low-carbon development. To fully utilize the limited resources in the virtual power plant planning stage, a two-sided match between VPPs and distributed energy companies is needed to better implement resource aggregation management. Because of the vagueness in this matching environment, the probabilistic linguistic term set (PLTS) is necessary to apply to express the decision makers’ preference. Considering the complex social relationships and intense competition among companies, a dynamic social network two-sided matching model is proposed for solving the multi-attribute two-sided matching decision-making problem. Firstly, we present a matching satisfaction degree described by PLTS. A dynamic social trust degree based on the sliding time concept is proposed. Secondly, the social trust network relationships are built based on the direct and indirect dynamic trust degree among companies. This relationship is then combined with an improved trust rank algorithm to identify the most authoritative and the most trusted company to provide the target company with a recommendation for the next moment. Besides, given that companies compete for limited resources, we further define the competitive satisfaction degree and apply the two-sided matching model. Additionally, then a two-sided matching model is developed. Finally, our model is tested numerically to ensure its accuracy and reliability.

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