A new bounded confidence model seeking structural balance

In this letter, we propose a novel model of opinion dynamics which takes into account the notions of latitude of acceptance, latitude of noncommitment, and latitude of rejection from social judgment theory. We examine the asymptotic behavior of the proposed model. Moreover, introduction of latitude of rejection and as a result negative interactions may render the influence graph unbalanced. Thus, we study the structural property of the influence graph. We prove that the proposed model eventually seeks a structurally balanced influence graph. Numerical examples are provided to further clarify the results.