Dynamics of linguistic opinion formation in bounded confidence model

Opinion dynamics is a fusion process of individual opinions based on the established fusion rules. The existing opinion dynamics models assume that agents express and receive their opinions in a numerical way. In this paper, we focus on the opinion formation in linguistic environment (i.e., linguistic opinion formation), and propose a linguistic opinion dynamics (LOD) model in the framework of the bounded confidence and the 2-tuples linguistic model with numerical scales. In the LOD model, agents express and receive the opinions by using the simple terms in a linguistic term set with finite granularity at each time. Based on the LOD model, we present some theoretical analyses to reveal the conditions to form a consensus or splits in the linguistic opinion formation. Furthermore, we design some simulations to investigate the effects of the bounded confidence and the uniformities of linguistic term sets on the linguistic opinion formation. The simulation results show that: (i) with the increase in the bounded confidence and the uniformities of linguistic term sets, the opportunity for reaching a consensus will increase, and the time for reaching a consensus will become shorter in the dynamics of linguistic opinion formation; (ii) there exists a critical point in the evolution of linguistic opinions, which is called agreed confidence in this paper, and a consensus among the agents will be reached if the value of the bounded confidence is equal or greater than the agreed confidence.