Recently, belief system dynamics has been proposed to model the opinion evolution of a social group on a set of logically interdependent topics (captured by a logic matrix). To analyze the evolution of belief system after a social group embeds into another social group when the two social groups have different ideologies on the logic dependence of topics, we creatively propose an extended multidimensional DeGroot model, which is modeled as the co-evolution of belief systems of two factions under social embedding, where the logic matrices of the two factions are considered as coherently heterogeneous and non-coherently heterogeneous. Through strict theoretical analysis for the proposed model, we demonstrate that social embedding can change a faction's belief system and quantify the effect under the two heterogeneities. Then, based on social embedding, we propose an embedding method of social robot to guide online public opinion. This method achieves the purpose of controlling online public opinion by establishing oneway communication from leaders in the social network to the social robot and adaptively controlling the belief system of the social robot. To verify the theoretical analysis results and supplement some new findings, we perform simulations to explore the impact of the number of social embeddings and the self-confidence degree of the social group on the time required for the belief system to reach stable state.& COPY; 2023 Elsevier B.V. All rights reserved.
