The formation of public opinion is typically influenced by different stakeholders, such as governments and firms. Recently, various real-world problems related to the management of public opinion have emerged, necessitating stakeholders to strategically allocate resources on networks to achieve their objectives. To address this, it is imperative to consider the dynamics of opinion formation. Notably, in existing opinion dynamics models, individuals possess self-confidence parameters reflecting their adherence to historical opinions. However, most extant studies assume the individuals’ self-confidence levels remain constant over time, which cannot accurately capture the intricacies of human behavior. In response to this gap, we first introduce a self-confidence evolution model, which encompasses two influencing factors: the self-confidence levels of one's group mates and the passage of time. Furthermore, we present the social network DeGroot model with self-confidence evolution, and conduct some theoretical analyses. Moreover, we propose a game model to identify the optimal resource allocation strategies of players on a network. Finally, we provide sensitivity analyses, comparative studies, and a case study. This paper highlights the significance of incorporating self-confidence evolution into the process of opinion dynamics, and the results can provide valuable practical insights for players seeking to improve their optimal resource allocation on a network to more effectively manage public opinions.

The evolution of opinion in Internet social networks may result in several risk issues in digital era, which have garnered government attention, and develop in business. This chapter proposes an index to measure the risk level in opinion evolution within the framework of the SNDG model and then presents the upper and lower bounds of risks determined by the social network structures. Furthermore, the social network risk control (SNRC) model is developed to control risk evolution by adding minimum interactions; some desired properties of the SNRC model are presented and discussed.

With the development of the information and Internet technology, the public opinions with big data will rapidly emerge in an online-offline social network, and an inefficient management of public opinions often will lead to the security crisis for either firms or governments. To unveil the interaction mechanism among a large number of agents between the online and offline social networks, in this paper we propose the public opinion dynamics model in an online-offline social network context. Next, in the theory aspect we investigate the analytical conditions to form a consensus in the public opinion dynamics model. Furthermore, we conduct the extensive simulations to investigate how the online agents impact the dynamics of public opinion formation, and unfold that the online agents shorten the steady-state time, decrease the number of opinion clusters, and smoothen the opinion changes in the opinion dynamics. The increase in the size of the online agents often enhances these effects. The results in this paper can provide a basis for the management of the public opinions in the Internet age.

In this paper, we investigate how the agent's self-confidence level and the node degree influence the consensus opinion formation and the consensus convergence speed in the social network DeGroot model. We find that (1) the higher self-confidence will increase the agent's importance degree to determine the consensus opinion, but will also slow down the convergence speed for all agents to be able to obtain consensus, and (2) it is conducive to accelerating the convergence speed to be able to reach a consensus where all agents can manage to balance self-confidence levels and node degrees in the social network.

When people express their opinions for an issue, they can express both exact opinions and uncertain opinions, such as numerical interval opinions. Moreover, social network is a crucial medium of opinion interaction and evolution. In this paper, uncertain opinion evolution with bounded confidence effects in social networks is investigated by theoretical demonstration and numerical examples analyses, and experiments simulations analyses. Theoretical results show when all the agents are with uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to decrease, even increase, as time increases; while when all the agents are without uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to increase, even decrease, as time increases. Moreover, the average widths of uncertain opinions are always smaller than the maximum opinion width of all the initial opinions among agents. Experiments simulations results show different ratios of agents with uncertainty tolerances and different ratios of agents expressing uncertain opinions have strong impact on the ratios of the agents expressing the uncertain opinions in the stable state, and the average widths of uncertain opinions in the stable state.

Nowadays, online social networks, such as “Facebook” and “WeChat,” facilitate the expression, diffusion, and interactions of individuals' opinions regarding various issues. In this environment, individuals' opinions are liable to be influenced by others and then evolve over the time. In this paper, we propose an approach based on minimum adjustments to manage the consensus in the group decision making (GDM) with opinions evolution. First, inspired by the idea proposed in DeGroot model, we establish a novel GDM model with opinions evolution, and then discuss its consensus conditions. Based on this, we propose an algorithm to achieve the network partition, and then provide a consensus model with minimum adjustments to obtain the optimal adjusted initial opinions and collective consensus opinion. Finally, we provide a numerical example to demonstrate the feasibility and effectiveness of the proposed theoretical results, and design comparative simulations to explore the effects of the opinions evolution on the final consensus solution.

2 online and offline environment in opinion dynamics, and we unfold that the asynchro-nization strongly impacts the consensus formation at complex networks: A high degree of the asynchronization makes it difficult for all agents to reach consensus in opinion dynamics. Furthermore, these effects are often further intensified as the number of online participating agents increases.

Nowadays, social networks facilitate individuals' expression of opinions about different political, economic and cultural issues, and firms or governments start to pay attentions on the management of public opinions, such as guiding the forming opinions to reach a specific consensus point. In this paper, we discuss that how to minimize the adjustments of individuals' initial opinions to reach a consensus with an established goal from the perspective based on opinion dynamics in social network.

Opinion dynamics is a fusion process of individual opinions, in which a group of interacting agents continuously fuse their opinions on the same issue based on established fusion rules to reach a consensus, polarization, or fragmentation in the final stage. To date, many studies have been conducted on opinion dynamics. To provide a clear perspective on the fusion process in opinion dynamics, this paper presents a review of the framework and formulation of opinion dynamics as well as some basic models, extensions, and applications. Based on the insights gained from prior studies, several open problems are proposed for future research.

Nowadays, with the development of information communication technology and Internet, more and more people receive information and exchange their opinions with others via online environments (e.g. Twitter, Facebook, Weibo, and WeChat). According to eMarketer Report [Worldwide Internet and Mobile Users: eMarketer’s Updated Estimates and Forecast for 2015–2020 (eMarketer Report). Published October 11, 2016, https://www.emarketer.com/Report/Worldwide-Internet-Mobile-Users-eMarketers-Updated-Estimates-Forecast-20152020/2001897 ).], by the end of 2016, more than 3.2 billion individuals worldwide will use the Internet regularly, accounting for nearly 45% of the world population. By contrast, the other half of the global population still obtain information and regularly exchange their opinions in a more traditional way (e.g. face to face). Generally, the speed at which information spreads and opinions are exchanged and updated in an online environment is much faster than in an offline environment. This paper focuses on jointly investigating the challenge of consensus formation in opinion dynamics with online and offline interactions. Without loss of generality, we assume the speed at which information spreads and opinions are exchanged and updated in an online environment is [Formula: see text] times as fast as in an offline environment. We demonstrate that the update speed ratio in mixed online and offline environments (i.e. [Formula: see text]) strongly impacts the consensus formation at complex networks: a large update speed ratio of online and offline environments (i.e. [Formula: see text]) makes it difficult for all agents to reach consensus in opinion dynamics. Furthermore, these effects are often further intensified as the number of online participating agents increases.

The methodology to solve the multiple attribute decision making (MADM) with preference information on alternatives has been systematically investigated. However, the inconsistency issue between the two rankings respectively derived from the preference information and the decision matrix is seldom considered. In order to investigate this issue, this paper proposes a consistency-based approach to MADM with preference information on alternatives. Based on the classical idea of the geometric consistency index in the preference relation, we define a geometric consistency index in MADM. Then, we propose an algorithm to adjust the preference information and the decision matrix simultaneously to improve the geometric consistency index in MADM. Next, some simulations experiments are designed to discuss the properties of the proposed approach. Finally, through illustrative examples and a comparative analysis, we demonstrate the effectiveness of the proposed approach.

Opinion dynamics investigates the fusion process of the opinion formation in a group of agents, and is a powerful tool for supporting the management of public opinions. However, in real-life situations, firms or administrations are not only interested in the formation of public opinions, but also hope to influence and guide the forming opinions to reach either a consensus or even more a specific consensus point. This paper aims at developing a consensus building process in opinion dynamics, based on the concept leadership, by analyzing the structure of the social network in which all agents can form a consensus. It is then proposed a strategy adding a minimum number of interactions in the social network to form a consensus based on leadership, and afterwards it is generalized the consensus strategy to deal with the consensus problem with an established target. Eventually, detailed theoretical proofs and numerical analysis are provided to demonstrate the feasibility and effectiveness of the consensus strategy.

Nowadays, about half of the world population can receive information and exchange opinions in online environments (e.g. the Internet), while the other half do so offline (e.g. face to face). The speed at which information is received and opinions are exchanged in online environment is much faster than offline. To model this phenomenon, in this paper we consider online and offline as two subsystems in opinion dynamics and assume asynchronization when agents in these two subsystems update their opinions. We unfold that asynchronization has a strong impact on the steady-state time of the opinion dynamics, the opinion clusters and the interactions between online and offline subsystems. Furthermore, these effects are often enhanced the larger the size of the online subsystem is.

Opinion dynamics provides a modeling tool for the public opinion management. The existing studies mainly focused on building the evolution model of opinions. However, the control of public opinions has been a key problem in practical opinion dynamics. The objective of this paper is to propose an opinion control rule to support the consensus reaching. Based on the bounded confidence model, the consensus model with the minimum adjustment is proposed. Next, based on the proposed consensus model, we propose the opinion control rule to support the consensus reaching. Furthermore, a numerical example is given to illustrate the feasibility of the proposed opinion control rule. Through simulation experiments, we investigate the effects of adjustment thresholds and bounded confidences on the opinion control rule.

Ideological and political education,as one of practices of humans,is a special field of human study on creating beauty and appreciating beauty,which should reform the subjective world of humans according to the law of beauty.This paper tries to define the beauty of ideological and political education and clarify the source of history of this kind of beauty,then under the guidance of this,the article attempts to create the beauty of ideological and political education.