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In this paper, we propose a novel opinion dynamics model that is based on bounded confidence and termed interval opinion dynamics with the dynamic bounded confidence. In this opinion dynamics model, the agents express their opinions in numerical intervals, and the bounded confidences vary in a specified interval as time varies (i.e., dynamic bounded confidence). Based on several theoretical analyses of the proposed opinion dynamics, we propose conditions that are sufficient to form a consensus or fragmentations among the agents. Moreover, we also design several simulation experiments to investigate the effects of the dynamic bounded confidence and interval widths on the proposed opinion dynamics and to illustrate the differences between the proposed model and the original opinion dynamics with bounded confidence.

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