Hesitant Fuzzy DeGroot Opinion Dynamics Model and Its Application in Multi-attribute Decision Making

  • Zhan Su
  • Zeshui Xu
  • Hua Zhao
  • Shousheng Liu


The research on the evolution law of the opinions can help the decision makers (DMs) improve the decision-making efficiency, predict the trend of events and make the right decision. These opinions are always described by one number, which is inaccurate and incomplete. To solve such a problem, in this paper, the hesitant fuzzy DeGroot (HF-DeGroot) opinion dynamics model is proposed. In order to simulate the transformation of hesitant fuzzy opinions, we introduced the multiplications for real matrix and hesitant fuzzy matrix. Then three kinds of transformation matrices with the consideration of the similarity degree, self-confidence degree and authority degree are constructed based on the hesitant fuzzy data and the consensus condition for the model is discussed as well. Furthermore, the HF-DeGroot opinion dynamics decision-making method is proposed from a prediction perspective and is applied to the emergency decision for the public health events. Finally, the effectiveness, feasibility and practicability of this method are shown by the comparison and simulation results.


[1] Araripe, L.E.; Filho, R. N. C.; Herrmann, H. J.; Andrade, J. S. (2006). Plurality voting: The statistical laws of democracy in brazil, International Journal of Modern Physics C, 17(12), 1809- 1813, 2006.

[2] Askarzadeh, Z.; Fu, R.; Halder, A.; Chen, Y. X.; Georgiou, T. T. (2020). Stability theory of stochastic models in opinion dynamics, IEEE Transactions on Automatic Control, 65(2), 522- 533, 2020.

[3] Berger, R.; Berger, L. (1981). A necessary and sufficient condition for reaching a consensus using DeGroot's method, Journal of the American Statistical Association, 76(374), 415-418, 1981.

[4] Bernardes, A. T.; Stauffer, D.; Kertész, J. (2002). Election results and the Sznajd model on Barabasi network, European Physical Journal B Condensed Matter, 25(1), 123-127, 2002.

[5] Binder, K. (1981). Finite size scaling analysis of ising model block distribution functions, Zeitschrift Für Physik B Condensed Matter, 43(2), 119-140, 1981.

[6] Chen, N.; Xu, Z. S.; Xia, M. M. (2013). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Applied Mathematical Modelling, 37(4), 2197-2211, 2013.

[7] Chettibi, S. (2020). Combination of HF set and MCDM for stable clustering in VANETs, IET Intelligent Transport Systems, 14(3), 190-195, 2020.

[8] Dahooie, J. H.; Vanaki, A. S.; Firoozfar, H. R.; Zavadskas, E. K.; Cereska, A. (2020). An extension of the failure mode and effect analysis with hesitant fuzzy sets to assess the occupational hazards in the construction industry, International Journal of Environmental Research and Public Health, 17(4), 2020.

[9] DeGroot, M. H. (1974). Reaching a consensus, Journal of the American Statistical Association, 69(345), 118-121, 1974.

[10] Ding, Z. G.; Chen, X.; Dong, Y. C.; Herrera. F. (2019). Consensus reaching in social network DeGroot model: the roles of the self-confidence and node degree, Information Sciences, 486, 62-72, 2019.

[11] Fortunato, S. (2005). On the consensus threshold for the opinion dynamics of krause-hegselmann, International Journal of Modern Physics C, 16(2), 259-270, 2005.

[12] Glauber, R. J. (1963). Time-dependent statistics of the Ising model, Journal of Mathematical Physics, 4(2), 294-307, 1963.

[13] Hegselmann, R.; Krause, U. (2002). Opinion dynamics and bounded confidence: Models, analysis, and simulation, Journal of Artifical Societies and Social Simulation, 5(3), 2002.

[14] Liao, H. C.; Xu, Z. S.; Xia, M. M. (2014). Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, International Journal of Information Technology and Decision Making, 13(1), 47-76, 2014.

[15] Marshall, A. W.; Olkin, I. (1979). Inequalities: Theory of majorization and its applications, Academic Press, 1979.

[16] Mo, X. Y.; Zhao, H.; Xu, Z. S. (2020). Feature-based hesitant fuzzy aggregation methods for satisfaction with life scale, Applied Soft Computing, Technique Report (2020).

[17] Proskurnikov, A. V.; Tempo, R. (2017). A tutorial on modeling and analysis of dynamic social networks. Part I, Communications of the ACM, 43, 65-79, 2017.

[18] Schulze, C.(2002). Advertising effects in Sznajd marketing model, Papers, 2002.

[19] Schneider, J. J.; Hirtreiter, C. (2005). The impact of election results on the member numbers of the large parties in bavaria and germany, International Journal of Modern Physics C, 16(8), 1165-1215, 2005.

[20] Seneta, E. (1981). Non-negative matrices and Markov chains, Springer-Verlag, 1981.

[21] Slanina F.; Lavicka, H. (2003). Analytical results for the Sznajd model of opinion formation, The European Physical Journal B-Condensed Matter, 35(2), 279-288, 2003.

[22] Song, C. Y.; Xu, Z. S.; Zhang, Y. X.; Wang, X. X. (2020). Dynamic hesitant fuzzy Bayesian network and its application in the optimal investment port decision making problem of "twentyfirst century maritime silk road", Applied Intelligence, 2020.

[23] Sood V.; Redner, S. (2005). Voter model on heterogeneous graphs, Physical Review Letters, 94(17), 178701, 2005.

[24] Stamatelatos, G.; Gyftopoulos, S.; Drosatos, G.; Efraimidis, P. S. (2002). Revealing the political affinity of online entities through their Twitter followers, Information Processing & Management, 57(2), 2020.

[25] Sznajd-Weron, K.; Weron, R. (2002). A simple model of price formation, International Journal of Modern Physics C, 13(1), 115-123, 2002.

[26] Torra, V. (2010). Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), 529-539, 2010.

[27] Xia, M. M.; Xu, Z. S. (2011). Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning, 52(3), 395-407, 2011.

[28] Xu, Z. S.; Xia, M. M. (2011). Distance and similarity measures for hesitant fuzzy sets, Information Sciences, 181(11), 2128-2138, 2011.

[29] Xu, Z. S.; Zhang, X. L. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems, 52, 53-64, 2013.

[30] Xu, Z. S. (2014). Hesitant fuzzy sets theory, Springer International Publishing, 2014.

[31] Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8(3), 338-353, 1965.

[32] Zhang, X. L.; Xu, Z. S. (2014). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment, Knowledge-Based Systems, 61, 48-58, 2014.
How to Cite
SU, Zhan et al. Hesitant Fuzzy DeGroot Opinion Dynamics Model and Its Application in Multi-attribute Decision Making. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 15, n. 4, june 2020. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3888>. Date accessed: 25 oct. 2021. doi: https://doi.org/10.15837/ijccc.2020.4.3888.


Hesitant fuzzy set, Opinion dynamics, consensus, decision making, opinion transition matrix, DeGroot opinion dynamics model