A New Model of Efficiency-Oriented Group Decision and Consensus Reaching Support in a Fuzzy Environment

  • Dominika Gołuńska
  • Janusz Kacprzyk
  • Sławomir Zadrożny
Part of the Communications in Computer and Information Science book series (CCIS, volume 443)


We present a novel comprehensive model of a consensus reaching support system in the fuzzy context. We assume the individual fuzzy preferences, a fuzzy majority in group decision making, as proposed by Kacprzyk [9], some fuzzy majority based solution concepts in group decision making, notably fuzzy cores (cf. Kacprzyk [9]) and their choice function based representations by Kacprzyk and Zadrożny [15],[16], a soft degree of consensus by Kacprzyk and Fedrizzi [10],[11]. Using as a point of departure Kacprzyk and Zadrożny’s [18] approach of the use of linguistic data summaries to support the running of a consensus reaching process, we develop and implement a novel approach that synergistically combines the tools and techniques mentioned above. We assume that moderated consensus reaching process which is run in the group of agents by a special agent called a moderator, is the most effective and efficient solution. We attempt to facilitate the work of a moderator, by some useful guidelines and additional indicators. We extend this idea and finally, we present a new implementation followed by a numerical evaluation of the new model proposed.


consensus reaching group decision support systems fuzzy preference relations soft degree of consensus linguistic quantifier fuzzy cores 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carlsson, C., Fedrizzi, M., Fuller, R.: Group Decision Support Systems. In: Carlsson, C., Fedrizzi, M., Fuller, R. (eds.) Fuzzy Logic in Management, vol. 66, ch. 3, Springer (2004)Google Scholar
  2. 2.
  3. 3.
    Fedrizzi, M., Kacprzyk, J., Nurmi, H.: Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators. Control and Cybernetics 22, 71–80 (1993)MathSciNetGoogle Scholar
  4. 4.
    Fedrizzi, M., Kacprzyk, J., Owsiński, J.W., Zadrożny, S.: Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles. Annals of Operations Research 51, 127–139 (1994)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fedrizzi, M., Kacprzyk, J., Zadrożny, S.: An interactive multi-user decision support system for consensus reaching process using fuzzy logic with linguistic quantifiers. Decision Support Systems 4(3), 313–327 (1988)CrossRefGoogle Scholar
  6. 6.
    Gołuńska, D., Kacprzyk, J.: The Conceptual Framework of Fairness in Consensus Reaching Process Under Fuzziness. In: Proceedings of the 2013 Joint IFSA World Congress NAFIPS Annual Meeting, Edmonton, Canada, June 24-28, pp. 1285–1290 (2013)Google Scholar
  7. 7.
    Herrera-Viedma, E., García-Lapresta, J.L., Kacprzyk, J., Fedrizzi, M., Nurmi, H., Zadrożny, S. (eds.): Consensual Processes. STUDFUZZ, vol. 267. Springer, Heidelberg (2011)Google Scholar
  8. 8.
    Herrera-Viedma, E., Cabrerizo, F.J., Kacprzyk, J., Pedrycz, W.: A review of soft consensus models in a fuzzy environment. Information Fusion 17, 4–13 (2014)CrossRefGoogle Scholar
  9. 9.
    Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets and Systems 18, 105–118 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Kacprzyk, J., Fedrizzi, M.: A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research 34, 315–325 (1988)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Kacprzyk, J., Fedrizzi, M.: A ‘human-consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers. Mathematical Social Sciences 18, 275–290 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems 49, 21–31 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Kacprzyk, J., Nurmi, H., Fedrizzi, I.M. (eds.): Consensus under Fuzziness, pp. 55–83. Kluwer Academic Publishers, Boston (1996)Google Scholar
  14. 14.
    Kacprzyk, J., Zadrożny, S.: On the use of fuzzy majority for supporting consensus reaching under fuzziness. In: Proceedings of FUZZ-IEEE 1997 - Sixth IEEE International Conference on Fuzzy Systems, Barcelona, Spain, vol. 3, pp. 1683–1988 (1997)Google Scholar
  15. 15.
    Kacprzyk, J.J., Zadrożny, S.: Computing with words in decision making through individual and collective linguistic choice rules. International Journal of Uncertainty, Fuzziness and Knowledge – Based Systems 9, 89–102 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Kacprzyk, J., Zadrożny, S.: Collective choice rules in group decision making under fuzzy preferences and fuzzy majority: a unified OWA operator based approach. Control and Cybernetics 31(4), 937–948 (2002)zbMATHGoogle Scholar
  17. 17.
    Kacprzyk, J., Zadrożny, S.: An Internet-based group decision support system. Management VII(28), 4–10 (2003)Google Scholar
  18. 18.
    Kacprzyk, J., Zadrożny, S.: Supporting consensus reaching in a group via fuzzy linguistic data summaries. In: IFSA 2005 World Congress, Beijing, pp. 1746–1751. Tsinghua University Press/Springer (2005)Google Scholar
  19. 19.
    Kacprzyk, J., Zadrożny, S.: Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the Ordered Weighted Average Operators. International Journal of Intelligent Systems 24(1), 4–26 (2009)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kacprzyk, J., Zadrożny, S.: Soft computing and Web intelligence for supporting consensus reaching. Soft Computing 14(8), 833–846 (2010)CrossRefGoogle Scholar
  21. 21.
    Kacprzyk, J., Zadrożny, S.: Computing with words is an implementable paradigm: fuzzy queries, linguistic data summaries and natural language generation. IEEE Transactions on Fuzzy Systems 18(3), 461–472 (2010)CrossRefGoogle Scholar
  22. 22.
    Kacprzyk, J., Zadrożny, S., Fedrizzi, M., Nurmi, H.: On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives. In: Bustince, H., et al. (eds.) Fuzzy Sets and Their Extensions: Representations, Aggregation and Models. STUDFUZZ, vol. 220, pp. 263–295. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Kacprzyk, J., Zadrożny, S., Raś, Z.W.: How to support consensus reaching using action rules: a novel approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18(4), 451–470 (2010)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Nurmi, H., Kacprzyk, J.: On fuzzy tournaments and their solution concepts in group decision making. European Journal of Operational Research 51, 223–232 (1991)CrossRefzbMATHGoogle Scholar
  25. 25.
    Turban, E., Aronson, J.E., Liang, T.P.: Decision Support Systems and Intelligent Systems, 6th edn., pp. 11–19, 94-101.C. Prentice Hall (2005)Google Scholar
  26. 26.
    Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications 9, 149–184 (1983)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dominika Gołuńska
    • 1
    • 2
  • Janusz Kacprzyk
    • 2
  • Sławomir Zadrożny
    • 2
  1. 1.Department of Automatic Control and Information TechnologyCracow University of TechnologyCracowPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations