The vagueness in human opinions, the randomness in the interactions among individuals, and the nonlinearities in opinion updates are challenging issues in modeling opinion formation and consensus. In this paper, we address the theoretical foundation and the necessary conditions for the convergence of opinion formation\\\'s nonlinear dynamics to the true states. For this purpose, we extend a probabilistic fuzzy model of opinion formation to include the effect of perceiving random and vague media content on the uncertainty of individuals\\\' opinions. In this model, each individual faces an uncertain media that is statistically modeled. Hence the individual perceives a probabilistic fuzzy set of possible environmental states and shapes its probabilistic fuzzy opinion (belief) based on its perceptions and negotiations. Theoretical results reveal that the media contents should be statistically supportive of the true state and that the coefficients in the belief update algorithms should be selected within the extracted bounds for the perception aggregation process and the proposed optimistic and pessimistic assuring operators. Application to two networks with different sizes of 94 and 918 nodes with 1134 and 206869 edges, respectively, confirms these theoretical conclusions. These simulation results show that higher diversity is observed in the opinions of the highly connected individuals. Furthermore, convergence is delayed for the larger network, i.e. there remain few individuals with differing opinions until the late stages of convergence. It is also shown that model convergence to the true state may deteriorate if parameter settings do not adhere to the theoretically obtained bounds.

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