Numerical Interval Opinion Dynamics in Social Networks: Stable State and Consensus

When people express their opinions, they often cannot provide the exact opinions but express uncertain opinions. Moreover, due to the differences in culture backgrounds and characters of agents, people who encounter uncertain opinions often show different uncertainty tolerances. By taking different uncertain opinions and different uncertainty tolerances into account, in this study we propose a numerical interval opinion dynamics model to investigate the process of forming collective opinions in a group of interaction agents under uncertain and social network context. We propose the theoretical analysis and algorithms to identify the stable agents whose opinions will be becoming stable and the oscillation agents whose opinions will always be fluctuate in the opinion evolution process. Furthermore, we study the conditions under which a consensus opinion can be building among the stable agents, and estimate the opinions ranges of the oscillation agents. Finally, numerical examples and analysis are used to show the feasibility and effectiveness of the proposed theories and algorithms.