Generating Recommendations in GDM with an Allocation of Information Granularity

  • Francisco Javier Cabrerizo
  • Juan Antonio Morente-Molinera
  • Sergio Alonso
  • Ignacio Javier Pérez
  • Raquel Ureña
  • Enrique Herrera-Viedma
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 581)


A Group decision making process is carried out when human beings jointly make an election from a possible collection of alternatives. Here, a question of importance is to avoid winners and losers, in the sense that the choice is not any more attributable to any single individual, but all group members contribute to the decision. For this reason, the agreement or consensus achieved among all the individuals should be as high as possible. In this contribution, a feedback mechanism is presented in order to increase the consensus achieved among the decision makers involved in this kind of problems. It is based on granular computing, which is utilized here to provide the necessary flexibility to increase the consensus. The feedback mechanism is able to deal with heterogeneous contexts, that is, contexts in which the decision makers have importance degrees considering their capacity or talent to handle the problem.


Group decision making Consensus Feedback mechanism Granular computing Heterogeneous contexts 



The authors would like to acknowledge FEDER financial support from the Projects TIN2013-40658-P and TIN2016-75850-P.


  1. 1.
    Bordogna, G., Fedrizzi, M., Pasi, A.: A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 27(1), 126–133 (1997)CrossRefGoogle Scholar
  2. 2.
    Butler, C.T., Rothstein, A.: On Conflict and Consensus: A Handbook on Formal Consensus Decision Making. Tahoma Park (2006)Google Scholar
  3. 3.
    Cabrerizo, F.J., Moreno, J.M., Pérez, I.J., Herrera-Viedma, E.: Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput. 14(5), 451–463 (2010)CrossRefGoogle Scholar
  4. 4.
    Cabrerizo, F.J., Heradio, R., Pérez, I.J., Herrera-Viedma, E.: A selection process based on additive consistency to deal with incomplete fuzzy linguistic information. J. Univ. Comput. Sci. 16(1), 62–81 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst. 97(1), 33–48 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chiclana, F., Herrera, F., Herrera-Viedma, E.: A note on the internal consistency of various preference representations. Fuzzy Sets Syst. 131(1), 75–78 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chen, S.J., Hwang, C.L.: Fuzzy Multiple Attributive Decision Making: Theory and its Applications. Springer, Berlin (1992)CrossRefGoogle Scholar
  8. 8.
    Chu, J., Liu, X., Wang, Y., Chin, K.-S.: A group decision making model considering both the additive consistency and group consensus of intuitionistic fuzzy preference relations. Comput. Ind. Eng. 101, 227–242 (2016)CrossRefGoogle Scholar
  9. 9.
    Deza, M.M., Deza, E.: Encyclopedia of Distances. Springer, Berlin (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Dong, Y., Xiao, J., Zhang, H., Wang, T.: Managing consensus and weights in iterative multiple-attribute group decision making. Appl. Soft Comput. 48, 80–90 (2016)CrossRefGoogle Scholar
  11. 11.
    Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer, Dordrecht (1994)CrossRefzbMATHGoogle Scholar
  12. 12.
    Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 7(1), 73–87 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets Syst. 88(1), 31–49 (1997)CrossRefzbMATHGoogle Scholar
  14. 14.
    Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making. Int. J. Approx. Reason. 16(3–4), 309–334 (1997)CrossRefzbMATHGoogle Scholar
  15. 15.
    Herrera-Viedma, E., Herrera, F., Chiclana, F.: A consensus model for multiperson decision making with different preference structures. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 32(3), 394–402 (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Herrera-Viedma, E., Martínez, L., Mata, F., Chiclana, F.: A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans. Fuzzy Syst. 3(5), 644–658 (2005)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefzbMATHGoogle Scholar
  19. 19.
    Herrera-Viedma, E., Herrera, F., Alonso, S.: Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 37(1), 176–189 (2007)CrossRefzbMATHGoogle Scholar
  20. 20.
    Herrera-Viedma, E., Cabrerizo, F.J., Kacprzyk, J., Pedrycz, W.: A review of soft consensus models in a fuzzy environment. Inf. Fusion 17, 4–13 (2014)CrossRefGoogle Scholar
  21. 21.
    Kacprzyk, J., Fedrizzi, M.: ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control Cybern. 15(3–4), 309–323 (1986)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Kacprzyk, J., Fedrizzi, M.: A ’soft’ measure of consensus in the setting of partial (fuzzy) preferences. Eur. J. Oper. Res. 34(3), 316–325 (1988)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst. 49(1), 21–31 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  25. 25.
    Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  26. 26.
    Ma, L.-C.: A new group ranking approach for ordinal preferences based on group maximum consensus sequences. Eur. J. Oper. Res. 251(1), 171–181 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Orlovski, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Pérez, I.J., Cabrerizo, F.J., Alonso, S., Herrera-Viedma, E.: A new consensus model for group decision making problems with non-homogeneous experts. IEEE Trans. Syst. Man Cybern.: Hum. 44(4), 494–498 (2014)CrossRefGoogle Scholar
  29. 29.
    Pedrycz, W.: The principle of justifiable granularity and an optimization of information granularity allocation as fundamentals of granular computing. J. Inf. Process. Syst. 7(3), 397–412 (2011)CrossRefGoogle Scholar
  30. 30.
    Pedrycz, A., Hirota, K., Pedrycz, W., Dong, F.: Granular representation and granular computing with fuzzy sets. Fuzzy Sets Syst. 203, 17–32 (2012)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Pedrycz, W.: Knowledge management and semantic modeling: a role of information granularity. Int. J. Softw. Eng. Knowl. 23(1), 5–12 (2013)CrossRefGoogle Scholar
  32. 32.
    Saint, S., Lawson, J.R.: Rules for Reaching Consensus: A Moderm Approach to Decision Making. Jossey-Bass, San Francisco (1994)Google Scholar
  33. 33.
    Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 12(2), 117–131 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85, 317–325 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Wang, X., Pedrycz, W., Gacek, A., Liu, X.: From numeric data to information granules: a design through clustering and the principle of justifiable granularity. Knowl.-Based Syst. 101, 100–113 (2016)CrossRefGoogle Scholar
  36. 36.
    Ureña, M.R., Cabrerizo, F.J., Morente-Molinera, J.A., Herrera-Viedma, E.: GDM-R: a new framework in R to support fuzzy group decision making processes. Inf. Sci. 357, 161–181 (2016)CrossRefGoogle Scholar
  37. 37.
    Wu, Z., Xu, J.: Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65, 28–40 (2016)CrossRefGoogle Scholar
  38. 38.
    Yager, R.R.: Weighted maximum entropy owa aggregation with applications to decision making under risk. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 39(3), 555–564 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Francisco Javier Cabrerizo
    • 1
  • Juan Antonio Morente-Molinera
    • 2
  • Sergio Alonso
    • 3
  • Ignacio Javier Pérez
    • 4
  • Raquel Ureña
    • 4
  • Enrique Herrera-Viedma
    • 1
  1. 1.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain
  2. 2.Universidad Internacional de La Rioja (UNIR)LogroñoSpain
  3. 3.Department of Software EngineeringUniversity of GranadaGranadaSpain
  4. 4.Department of Computer Science and EngineeringUniversity of CádizCádizSpain

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