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Modeling the Social Influence in Consensus Reaching Process with Interval Fuzzy Preference Relations

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Abstract

Consensus process plays a prominent role in decision-making problems. In traditional way, experts with low consensus degree are asked to modify their opinions according to the given advices. However, in fact, experts neither simply adopt nor completely ignore the opinions of others. In general, experts will refer to other experts’ opinions to a certain extent and their opinions will evolve due to their interactions. The aim of this paper, therefore, is to propose a consensus model based on uncertain opinion evolution to model the influence between experts during the negotiation and communication process. Firstly, we construct an influence network among experts by taking both objective similarity degree and some subjective psychological traits into consideration. Secondly, a consensus model based on opinion evolution with interval fuzzy preference relations (IFPRs) is proposed. After identifying the incompatible preference with lower consensus degree, experts will modify their preferences according to the preference evolution under the influence network. Then, we prove that the reciprocity property maintains through the dynamic consensus reaching process, and a sufficient condition guaranteeing that the consensus can be reached in the influence network is derived. Furthermore, two nonlinear programming models are proposed to justify whether the IFPR satisfies the acceptable consistency and to calculate the priority vector of the IFPR, respectively. Finally, a case study and comparative analysis are made to illustrate the effectiveness of the proposed model.

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References

  1. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. The Macmilan press LTD, London (1976)

    Book  MATH  Google Scholar 

  2. Bezdek, J.C., Spillman, B., Spillman, R.: A fuzzy relation space for group decision theory. Fuzzy Set Syst. 1(4), 255–268 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. Basu, R., Sly, A.: Evolving voter model on dense random graphs. Ann. Appl. Probab. 27(2), 1235–1288 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Barker, T.J., Zabinsky, Z.B.: A multicriteria decision making model for reverse logistics using analytical hierarchy process. Omega 39(5), 558–573 (2011)

    Article  Google Scholar 

  5. Cabrerizo, F.J., Chiclana, F., Al-Hmouz, R., Morfeq, A., Balamash, A.S., Herrera-Viedma, E.: Fuzzy decision making and consensus: challenges. J. Intell. Fuzzy Syst. 29(3), 1109–1118 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chiclana, F., Herrera-Viedma, E., Alonso, S., Herrera, F.: Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Trans. Fuzzy Syst. 17(1), 14–23 (2009)

    Article  Google Scholar 

  7. Castro, J., Lu, J., Zhang, G.Q., Dong, Y.C., Martínez, L.: Opinion dynamics based group recommender systems. IEEE Trans. Syst. Man Cybern. Syst. 48(12), 2394–2406 (2018)

    Article  Google Scholar 

  8. Capuano, N., Chiclana, F., Fujta, H., Herrera-Viedma, E., Loia, V.: Fuzzy group decision making with incomplete information guided by social influence. IEEE Trans. Fuzzy Syst. 26(3), 1704–1718 (2018)

    Article  Google Scholar 

  9. Dittmer, J.C.: Consensus formation under bounded confidence. Nonlinear Anal. 47, 4615–4621 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Degroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 122, 118–121 (1974)

    Article  MATH  Google Scholar 

  11. Dong, Q.X., Cooper, O.: A peer-to-peer dynamic adaptive consensus reaching model for the group AHP decision making. Eur. J. Oper. Res. 250, 521–530 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dong, Y.C., Ding, Z.G., Chiclana, F., Herrera-Viedma, E.: Dynamics of public opinions in an online and offline social network. IEEE Trans. Big Data (2017). https://doi.org/10.1109/TBDATA.2017.2676810

    Article  Google Scholar 

  13. Dong, Y.C., Ding, Z.G., Martínez, L., Herrera, F.: Managing consensus based on leadership in opinion dynamics. Inf. Sci. 397, 187–205 (2017)

    Article  Google Scholar 

  14. Dong, Y.C., Zha, Q.B., Zhang, H.J., Kou, G., Ding, Z.G., Liang, H.M.: A survey on the fusion process in opinion dynamic. Inf. Fusion 43, 57–65 (2018)

    Article  Google Scholar 

  15. Dong, Y.C., Zhan, M., Kou, G., Fujita, H., Chiclana, F., Herrera-Viedma, E.: Consensus reaching in social network group decision making: research paradigms and challenges. Knowl. Based Syst. (2018). https://doi.org/10.1016/j.knosys.2018.06.036

    Article  Google Scholar 

  16. Friedkin, N., Johnsen, E.: Social influence nerwork and opinion change. Adv. Group Decis. Process. 16(1), 1–29 (1999)

    Google Scholar 

  17. Gupta, M.: Consensus building process in group decision making-an adaptive procedure based on group dynamics. IEEE Trans. Fuzzy Syst. 26(4), 1923–1933 (2018)

    Article  Google Scholar 

  18. Gong, Z.W., Zhang, H.H., Forrest, J., Li, L.S., Xu, X.X.: Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual. Eur. J. Oper. Res. 240(1), 183–192 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gong, Z.W., Tan, X., Yang, Y.J.: Optimal weighting models based on linear uncertain constraints in intuitionistic fuzzy preference relations. J. Oper. Res. Soc. (2018). https://doi.org/10.1080/01605682.2018.1489349

    Article  Google Scholar 

  20. Gong, Z.W., Zhang, N., Chiclana, F.: The optimization ordering model for intuitionistic fuzzy preference relations with utility functions. Knowl. Based Syst. 162(15), 174–184 (2018)

    Article  Google Scholar 

  21. Gong, Z.W., Forrest, J., Yang, Y.J.: The optimal group consensus models for 2-tuple linguistic preference relations. Knowl. Based Syst. 37, 427–437 (2013)

    Article  Google Scholar 

  22. Herrera-Viedma, E., Alonso, S., Chiclana, F., Herrera, F.: A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst. 15(5), 863–877 (2007)

    Article  MATH  Google Scholar 

  23. Herrera-Viedma, E., Herrera, F., Chiclana, F., Luque, M.: Some issues on consistency of fuzzy preference relations. Eur. J. Oper. Res. 154(1), 98–109 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. Herrera, F., Martínez, L., Sánchez, P.J.: Managing non-homogeneous information in group decision making. Eur. J. Oper. Res. 166(1), 115–132 (2005)

    Article  MATH  Google Scholar 

  25. Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  26. Li, C.C., Rodríguez, R.M., Martínez, L., Dong, Y.C., Herrera, F.: Consensus building with individual consistency control in group decision making. IEEE Trans. Fuzzy Syst. 27(2), 319–332 (2019)

    Article  Google Scholar 

  27. Liu, F., Zhang, W.G., Fu, J.H.: A new method of obtaining the priority weights from an interval fuzzy preference relation. Inf. Sci. 185(1), 32–42 (2012)

    Article  MATH  Google Scholar 

  28. Liu, F., Zhang, W.G., Fu, J.H.: A new method of obtaining the priority weights from an interval fuzzy preference relation. Inf. Sci. 185(1), 32–42 (2012)

    Article  MATH  Google Scholar 

  29. Liu, F., Zhang, W.G., Zhang, L.H.: A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices. Fuzzy Sets Syst. 246(1), 1–18 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  30. Liang, Q., Liao, X., Liu, J.: A social ties-based approach for group decision-making problems with incomplete additive preference relations. Knowl. Based Syst. 119, 158–166 (2017)

    Article  Google Scholar 

  31. Liu, Y.J., Liang, C.Y., Chiclana, F., Wu, J.: A trust induced recommendation mechanism for reaching consensus in group decision making. Knowl. Based Syst. 119, 221–231 (2017)

    Article  Google Scholar 

  32. Orlovsky, S.A.: Decision making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  33. Palomares, I., Liu, J., Xu, Y., Martínez, L.: Modelling experts attitudes in group decision making. Soft Comput. 16, 1755–1766 (2012)

    Article  MATH  Google Scholar 

  34. Palomares, I., Martínez, L., Herrera, F.: A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans. Fuzzy Syst. 22(3), 516–530 (2014)

    Article  Google Scholar 

  35. Palomares, I., Estrella, F.J., Martínez, L., Herrera, F.: Consensus under a fuzzy context: taxonomy, analysis framework AFRYCA and experimental case of study. Inf. Fusion 20, 252–271 (2014)

    Article  Google Scholar 

  36. Pérez, L.G., Mata, F., Chiclana, F.: Social network decision making with linguistic trustworthiness-based induced OWA operators. Int. J. Intell. Syst. 29, 1117–1137 (2014)

    Article  Google Scholar 

  37. Pérez, L.G., Mata, F., Chiclana, F., Kou, G., Herrera-Viedma, E.: Modeling influence in group decision making. Soft Comput. 20(4), 1653–1665 (2016)

    Article  Google Scholar 

  38. Recio-García, J.A., Quijano, L., Díaz-Agudo, B.: Including social factors in an argumentative model for group decision support systems. Decis. Support Syst. 56, 48–55 (2013)

    Article  Google Scholar 

  39. Rodríguez, R.M., Labella, Á., Tré, G.D., Martínez, L.: A large scale consensus reaching process managing group hesitation. Knowl. Based Syst. 159, 86–97 (2018)

    Article  Google Scholar 

  40. Saaty, T.L.: The Analytical Hierarchy Process. McGrow-Hill, New York (1980)

    MATH  Google Scholar 

  41. Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 12, 117–131 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  42. Ureña, R., Chiclana, F., Melançon, G., Herrera-Viedma, E.: A social network based approach for consensus achievement in multiperson decision making. Inf. Fusion 47, 72–87 (2018). https://doi.org/10.1016/j.inffus.2018.07.006

    Article  Google Scholar 

  43. Wang, L.H., Gong, Z.W., Zhang, N.: Consensus modelling on interval-valued fuzzy preference relations with normal distribution. Int. J. Comput. Intell. Syst. 11(1), 706–715 (2018)

    Article  Google Scholar 

  44. Wang, T.C., Chen, Y.H.: Applying consistent fuzzy preference relations to partnership selection. Omega 35, 384–388 (2007)

    Article  Google Scholar 

  45. Wang, Z.G., Chen, Y.G.: Logarithmic least squares prioritization and completion methods for interval fuzzy preference relations based on geometric transitivity. Inf. Sci. 289, 59–75 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wang, Z.G.: A two-stage linear goal programming approach to eliciting interval weights from additive interval fuzzy preference relations. Soft Comput. 20(7), 2721–2732 (2016)

    Article  MATH  Google Scholar 

  47. Wei, C.P., Zhang, Y.Z., Feng, X.Q.: Deriving weights from interval comparison matrices based on consistency test. Syst. Eng. Theory Pract. 27, 132–139 (2007)

    Article  Google Scholar 

  48. Wu, J., Chiclana, F.: A social nerwork analysis trust-consensus based approach to group decision-making problems with interval value fuzzy reciprocal preference. Knowl. Based Syst. 59(2), 97–107 (2014)

    Article  Google Scholar 

  49. Wu, J., Xiong, R.Y., Chiclana, F.: Uninorm trust propagation and aggregation methods for group decision making in social network with four tuple information. Knowl. Based Syst. 96(2), 29–39 (2016)

    Google Scholar 

  50. Wu, J., Chiclana, F., Herrera-Viedma, E.: Trust based consensus model for social network in an incomplete linguistic information context. Appl. Soft Comput. 35, 827–839 (2015)

    Article  Google Scholar 

  51. Wu, J., Chiclana, F., Fujita, H., Herrera-Viedma, E.: A visual interaction consensus model for social network group decision making with trust propagation. Knowl. Based Syst. 122, 39–50 (2017)

    Article  Google Scholar 

  52. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Application. Cambridge University Press, Cambridge (1994)

    Book  MATH  Google Scholar 

  53. Xu, Y.J., Li, K.W., wang, H.M.: Incomplete interval fuzzy preference relations and their applications. Comput. Ind. Eng. 67(1), 93–103 (2014)

    Article  Google Scholar 

  54. Xu, Y.J., Wen, X.W., Sun, H., Wang, H.M.: Consistency and consensus models with local adjustment strategy for hesitant fuzzy linguistic preference relations. Int. J. Fuzzy Syst. 20(7), 2216–2233 (2018)

    Article  MathSciNet  Google Scholar 

  55. Xu, Y.J., Zhang, Z.Q., Wang, H.M.: A consensus-based method for group decision making with incomplete uncertain linguistic preference relations. Soft Comput. 23(2), 669–682 (2019)

    Article  MATH  Google Scholar 

  56. Xu, Z.S., Da, Q.L.: The uncertain OWA operator. Int. J. Intell. Syst. 17(6), 569–575 (2002)

    Article  MATH  Google Scholar 

  57. Xu, Z.S., Chen, J.: Some models for deriving the priority weights from interval fuzzy preference relations. Eur. J. Oper. Res. 184(1), 266–280 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  58. Xu, Z.S.: Consistency of interval fuzzy preference relations in group decision making. Appl. Soft Comput. 11(5), 898–909 (2011)

    Google Scholar 

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Acknowledgements

The work was partly supported by the National Natural Science Foundation of China (71371107, 71702087).

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Authors and Affiliations

  1. College of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Shengli Li & Cuiping Wei

  2. Department of Mathematics, Taiyuan Normal University, Jinzhong, 030619, China

    Shengli Li

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  1. Shengli Li
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  2. Cuiping Wei
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Correspondence to Cuiping Wei.

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Li, S., Wei, C. Modeling the Social Influence in Consensus Reaching Process with Interval Fuzzy Preference Relations. Int. J. Fuzzy Syst. 21, 1755–1770 (2019). https://doi.org/10.1007/s40815-019-00671-5

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