Many empirical networks are intrinsically pluralistic, with interactions occurring within groups of arbitrary agents. Then the agent in the network can be influenced by types of neighbors, common examples include similarity, opposition, and negligibility. Although the influence of neighbors can be described as an amicable and antagonistic relationship in complex real-world systems accurately, and the research on the dynamic process of public opinion evolution with different types of influence is valuable, few studies have mentioned that issue. In this paper, we develop a novel model on networks of agents with the bi-directional bounded thresholds for studying the evolution of opinion dynamics. We define the scope of individual assimilation and exclusion to identify different types of neighbors and calculate the impact of the corresponding neighbors on the individuals by converting the opinion difference. The simulation results show that the proposed mechanism can effectively explain the formation of bi-polarization during opinion evolution and the settings of the bi-directional bounded thresholds significantly influence the eventual distribution of opinions. Furthermore, we explore the impacts of the initial conditions and the structure of the small-world network on the evolution of opinions.