Uncertain Opinion Evolution with Bounded Confidence Effects in Social Networks

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.

[1]  Shui Yu,et al.  Linguistic Computational Model Based on 2-Tuples and Intervals , 2013, IEEE Transactions on Fuzzy Systems.

[2]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[3]  Irinel-Constantin Morarescu,et al.  Opinion dynamics aware marketing strategies in duopolies , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[4]  Felipe Bravo-Marquez,et al.  Opinion Dynamics of Elections in Twitter , 2012, 2012 Eighth Latin American Web Congress.

[5]  Emilio Hernández-García,et al.  The noisy Hegselmann-Krause model for opinion dynamics , 2013, 1309.2858.

[6]  Gerardo Iñiguez,et al.  Opinion and community formation in coevolving networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. Mendel,et al.  Fuzzy Opinion Networks: A Mathematical Framework for the Propagation of Opinions and Their Uncertainties Across Social Networks , 2014 .

[8]  Santo Fortunato.  Damage spreading and opinion dynamics on scale-free networks , 2005 .

[9]  Francisco Herrera,et al.  A Consensus Model for Large-Scale Linguistic Group Decision Making With a Feedback Recommendation Based on Clustered Personalized Individual Semantics and Opposing Consensus Groups , 2019, IEEE Transactions on Fuzzy Systems.

[10]  H. Micklitz,et al.  Superconductor-insulator transition tuned by annealing in Bi-film on top of Co-clusters , 2013 .

[11]  E. Herrera‐Viedma,et al.  The consensus models with interval preference opinions and their economic interpretation , 2015 .

[12]  Jan Lorenz.  Heterogeneous bounds of confidence: Meet, discuss and find consensus! , 2010 .

[13]  Enrique Herrera-Viedma,et al.  On dynamic consensus processes in group decision making problems , 2018, Inf. Sci..

[14]  Andre C. R. Martins,et al.  CONTINUOUS OPINIONS AND DISCRETE ACTIONS IN OPINION DYNAMICS PROBLEMS , 2007, 0711.1199.

[15]  Mehmet E. Yildiz,et al.  Competitive Targeted Advertising Over Networks , 2016, Oper. Res..

[16]  D. Stauffer,et al.  Election results and the Sznajd model on Barabasi network , 2001, cond-mat/0111147.

[17]  Francesco Bullo,et al.  How truth wins in opinion dynamics along issue sequences , 2017, Proceedings of the National Academy of Sciences.

[18]  Gang Kou,et al.  Consensus reaching in social network group decision making: Research paradigms and challenges , 2018, Knowl. Based Syst..

[19]  Francesco Bullo,et al.  Opinion Dynamics and the Evolution of Social Power in Influence Networks , 2015, SIAM Rev..

[20]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[21]  David H. Glass,et al.  Characteristics of successful opinion leaders in a bounded confidence model , 2016 .

[22]  Olivier Gibaru,et al.  Convergence Rate of the Causal Jacobi Derivative Estimator , 2010, Curves and Surfaces.

[23]  M. Degroot.  Reaching a Consensus , 1974 .

[24]  Francisco Herrera,et al.  Managing consensus based on leadership in opinion dynamics , 2017, Inf. Sci..

[25]  Guillaume Deffuant,et al.  Meet, discuss, and segregate! , 2002, Complex..

[26]  Ning Zhang,et al.  Consensus modeling with cost chance constraint under uncertainty opinions , 2017, Appl. Soft Comput..

[27]  Keith W. Hipel,et al.  Modeling Fuzzy and Interval Fuzzy Preferences Within a Graph Model Framework , 2016, IEEE Transactions on Fuzzy Systems.

[28]  Herbert Spohn,et al.  Hydrodynamics of the Voter Model , 1983 .

[29]  K. Sznajd-Weron,et al.  How effective is advertising in duopoly markets , 2002 .

[30]  Gang Kou,et al.  A survey on the fusion process in opinion dynamics , 2018, Inf. Fusion.

[31]  Yucheng Dong,et al.  The fusion process with heterogeneous preference structures in group decision making: A survey , 2015, Inf. Fusion.

[32]  R. Berger.  A Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot's Method , 1981 .

[33]  Jan Lorenz,et al.  Continuous Opinion Dynamics under Bounded Confidence: A Survey , 2007, 0707.1762.

[34]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[35]  Xiao Song,et al.  Opinion dynamics in networked command and control organizations , 2013 .

[36]  Gerardo Iñiguez,et al.  Dynamics of deceptive interactions in social networks , 2015, Journal of The Royal Society Interface.

[37]  J. French.  A formal theory of social power. , 1956, Psychology Review.

[38]  Roberto Tempo,et al.  Network science on belief system dynamics under logic constraints , 2016, Science.

[39]  Enrique Herrera-Viedma,et al.  Consensus Building for the Heterogeneous Large-Scale GDM With the Individual Concerns and Satisfactions , 2018, IEEE Transactions on Fuzzy Systems.

[40]  Liu Yijun,et al.  Opinion dynamics on triad scale free network , 2012, AMT 2012.

[41]  Noah E. Friedkin,et al.  Social influence and opinions , 1990 .

[42]  Vittorio Loreto,et al.  Opinion dynamics: models, extensions and external effects , 2016, Participatory Sensing, Opinions and Collective Awareness.

[43]  E.Ben-Naim,et al.  Coarsening and persistence in the voter model , 1995, cond-mat/9511040.

[44]  Keith W. Hipel,et al.  Interval fuzzy preferences in the graph model for conflict resolution , 2018, Fuzzy Optim. Decis. Mak..

[45]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[46]  Guido Caldarelli,et al.  Opinion dynamics on interacting networks: media competition and social influence , 2014, Scientific Reports.

[47]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[48]  P. Krapivsky,et al.  Coarsening and persistence in the voter model. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[49]  Ning Zhang,et al.  Consensus Modelling on Interval-Valued Fuzzy Preference Relations with Normal Distribution , 2018, Int. J. Comput. Intell. Syst..

[50]  Keith W. Hipel,et al.  Dominating attitudes in the graph model for conflict resolution , 2012 .

[51]  Muruhan Rathinam,et al.  Convergence, Stability, and Robustness of Multidimensional Opinion Dynamics in Continuous Time , 2018, SIAM J. Control. Optim..

[52]  Adrian Carro,et al.  The noisy voter model on complex networks , 2016, Scientific Reports.

[53]  Yucheng Dong,et al.  Dynamics of Uncertain Opinion Formation: An Agent-Based Simulation , 2016, J. Artif. Soc. Soc. Simul..

[54]  Yiguang Hong,et al.  Noise leads to quasi-consensus of Hegselmann-Krause opinion dynamics , 2015, Autom..

[55]  Masoud Asadpour,et al.  Opinion Formation by Informed Agents , 2015 .

[56]  Allan Sly,et al.  Evolving Voter Model on Dense Random Graphs , 2015, 1501.03134.

[57]  Kevin J. S. Zollman.  Social network structure and the achievement of consensus , 2012 .

[58]  Gang Kou,et al.  A review on trust propagation and opinion dynamics in social networks and group decision making frameworks , 2019, Inf. Sci..

[59]  Jerry M. Mendel,et al.  Fuzzy Opinion Networks: A Mathematical Framework for the Evolution of Opinions and Their Uncertainties Across Social Networks , 2014, IEEE Transactions on Fuzzy Systems.

[60]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[61]  Celia Anteneodo,et al.  Impact of contrarians and intransigents in a kinetic model of opinion dynamics , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[62]  Enrique Herrera-Viedma,et al.  Multiple Attribute Strategic Weight Manipulation With Minimum Cost in a Group Decision Making Context With Interval Attribute Weights Information , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[63]  Mehmet E. Yildiz,et al.  Binary Opinion Dynamics with Stubborn Agents , 2013, TEAC.

[64]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[65]  Enrique Herrera-Viedma,et al.  A Self-Management Mechanism for Noncooperative Behaviors in Large-Scale Group Consensus Reaching Processes , 2018, IEEE Transactions on Fuzzy Systems.

[66]  Janke Dittmer.  Consensus formation under bounded confidence , 2001 .