A consensus model for group decision making under interval type-2 fuzzy environment



We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.

Key words

Group decision making (GDM) Interval type-2 fuzzy sets (IT2 FSs) Feedback mechanism 

CLC number

O159 O22 


  1. Alonso, S., Herrera-Viedma, E., Chiclana, F., et al., 2010. A web based consensus support system for group decision making problems and incomplete preferences. Inform. Sci., 180(23):4477–4495. http://dx.doi.org/10.1016/j.ins.2010.08.005MathSciNetCrossRefGoogle Scholar
  2. Alonso, S., Pérez, I.J., Cabrerizo, F.J., et al., 2013. A linguistic consensus model for Web 2.0 communities. Appl. Soft Comput., 13(1):149–157. http://dx.doi.org/10.1016/j.asoc.2012.08.009CrossRefGoogle Scholar
  3. Cabrerizo, F.J., Moreno, J.M., Pérez, I.J., et al., 2010. Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput., 14(5):451–463. http://dx.doi.org/10.1007/s00500-009-0453-xCrossRefGoogle Scholar
  4. Cabrerizo, F.J., Herrera-Viedma, E., Pedrycz, W., 2013. A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur. J. Oper. Res., 230(3):624–633. http://dx.doi.org/10.1016/j.ejor.2013.04.046MathSciNetCrossRefGoogle Scholar
  5. Cabrerizo, F.J., Morente-Molinera, J.A., Pérez, I.J., et al., 2015a. A decision support system to develop a quality management in academic digital libraries. Inform. Sci., 323:48–58. http://dx.doi.org/10.1016/j.ins.2015.06.022MathSciNetCrossRefGoogle Scholar
  6. Cabrerizo, F.J., Chiclana, F., Al-Hmouz, R., et al., 2015b. Fuzzy decision making and consensus: challenges. J. Intell. Fuzzy Syst., 29(3):1109–1118. http://dx.doi.org/10.3233/IFS-151719MathSciNetCrossRefGoogle Scholar
  7. Chen, S.M., Lee, L.W., 2010. Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst. Appl., 37(1):824–833. http://dx.doi.org/10.1016/j.eswa.2009.06.094MathSciNetCrossRefGoogle Scholar
  8. Chen, Z., Yang, W., 2011. A new multiple attribute group decision making method in intuitionistic fuzzy setting. Appl. Math. Model., 35(9):4424–4437. http://dx.doi.org/10.1016/j.apm.2011.03.015MathSciNetCrossRefGoogle Scholar
  9. Chiclana, F., Tapia Garcia, J.M., Del Moral, M.J., et al., 2013. A statistical comparative study of different similarity measures of consensus in group decision making. Inform. Sci., 221:110–123. http://dx.doi.org/10.1016/j.ins.2012.09.014MathSciNetCrossRefGoogle Scholar
  10. Feng, Z.Q., Liu, C., Huang, H., 2014. Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(8):636–650. http://dx.doi.org/10.1631/jzus.C1300370CrossRefGoogle Scholar
  11. Herrera-Viedma, E., Alonso, S., Chiclana, F., et al., 2007. A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst., 15(5):863–877. http://dx.doi.org/10.1109/TFUZZ.2006.889952CrossRefGoogle Scholar
  12. Herrera-Viedma, E., Cabrerizo, F.J., Kacprzyk, J., et al., 2014. A review of soft consensus models in a fuzzy environment. Inform. Fus., 17:4–13. http://dx.doi.org/10.1016/j.inffus.2013.04.002CrossRefGoogle Scholar
  13. Lee, L.W., Chen, S.M., 2008. A new method for fuzzy multiple attributes group decision-making based on the arithmetic operations of interval type-2 fuzzy sets. Proc. 7th Int. Conf. on Machine Learning and Cybernetics, p.3084–3089. http://dx.doi.org/10.1109/ICMLC.2008.4620938Google Scholar
  14. Mata, F., Martínez, L., Herrera-Viedma, E., 2009. An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. IEEE Trans. Fuzzy Syst., 17(2):279–290. http://dx.doi.org/10.1109/TFUZZ.2009.2013457CrossRefGoogle Scholar
  15. Mendel, J.M., John, R.I., Liu, F., 2006. Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst., 14(6):808–821. http://dx.doi.org/10.1109/TFUZZ.2006.879986CrossRefGoogle Scholar
  16. Mendel, J.M., Zadeh, L.A., Trillas, E., et al., 2010. What computing with words means to me. IEEE Comput. Intell. Mag., 5(1):20–26. http://dx.doi.org/10.1109/MCI.2009.934561CrossRefGoogle Scholar
  17. Moharrer, M., Tahayori, H., Livi, L., et al., 2015. Interval type-2 fuzzy sets to model linguistic label perception in online services satisfaction. Soft Comput., 19(1):237–250. http://dx.doi.org/10.1007/s00500-014-1246-4CrossRefGoogle Scholar
  18. Pérez, I.J., Cabrerizo, F.J., Alonso, S., et al., 2014. A new consensus model for group decision making problems with non-homogeneous experts. IEEE Trans. Syst. Man Cybern. Syst., 44(4):494–498. http://dx.doi.org/10.1109/TSMC.2013.2259155CrossRefGoogle Scholar
  19. Sabahi, F., Akbarzadeh-T, M.R., 2014. A framework for analysis of extended fuzzy logic. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(7):584–591. http://dx.doi.org/10.1631/jzus.C1300217CrossRefGoogle Scholar
  20. Wang, W., Liu, X., Qin, Y., 2012. Multi-attribute group decision making models under interval type-2 fuzzy environment. Knowl.-Based Syst., 30:121–128. http://dx.doi.org/10.1016/j.knosys.2012.01.005CrossRefGoogle Scholar
  21. Wang, Z.J., Li, K.W., 2015. A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices. Eur. J. Oper. Res., 242(3):890–900. http://dx.doi.org/10.1016/j.ejor.2014.10.025MathSciNetCrossRefGoogle Scholar
  22. Wu, D., Mendel, J.M., 2011. On the continuity of type-1 and interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst., 19(1):179–192. http://dx.doi.org/10.1109/TFUZZ.2010.2091962CrossRefGoogle Scholar
  23. Wu, J., Chiclana, F., 2014. A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowl.-Based Syst., 59:97–107. http://dx.doi.org/10.1016/j.knosys.2014.01.017CrossRefGoogle Scholar
  24. Wu, J., Chiclana, F., Herrera-Viedma, E., 2015. Trust based consensus model for social network in an incomplete linguistic information context. Appl. Soft Comput., 35:827–839. http://dx.doi.org/10.1016/j.asoc.2015.02.023CrossRefGoogle Scholar
  25. Zhang, X., Ge, B., Jiang, J., et al., 2015. A new consensus model for group decision making using fuzzy linguistic preference relations with heterogeneous experts. J. Intell. Fuzzy Syst., 30(1):171–182. http://dx.doi.org/10.3233/IFS-151744CrossRefGoogle Scholar
  26. Zhang, Z., Zhang, S., 2013. A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl. Math. Model., 37(7):4948–4971. http://dx.doi.org/10.1016/j.apm.2012.10.006MathSciNetCrossRefGoogle Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of Information System and ManagementNational University of Defense TechnologyChangshaChina

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