A Consensus Reaching Support System for Multi-criteria Decision Making Problems

  • Dominika GołuńskaEmail author
  • Janusz Kacprzyk
Part of the Studies in Computational Intelligence book series (SCI, volume 634)


We present an extension of a consensus reaching support system presented in our previous works to additionally accommodate a multi-criteria evaluation of options and importance weights of all criteria given by each agent (individual). The multi-criteria setting implies a need for some modification of concepts, tools and techniques proposed in our previous works with a single criterion. To improve the efficiency of the process we use some additional suggestions/hints provided for the moderator in the form of linguistic summaries, modified to the multi-criteria setting. We present an application for a real world problem which involves reaching of a sufficient agreement in the small group of human agents. The results obtained are intuitively appealing, and promising in terms of time and costs of opinion changes to reach a sufficient consensus.


Multi-criteria decision making Consensus reaching process Group decision support system Linguistic data summaries Degree of consensus Linguistic preferences Moderator Measures of agreement 



This work is partially supported by the Foundation for Polish Science under the “International Ph.D. Projects in Intelligent Computing” financed from the Europe-an Union within the Innovative Economy Operational Programme 2007–2013 and European Regional Development Fund (D. Gołuńska), and partially by the National Science Centre under Grant No. UMO 2012/05/B/ST6/03068 (J. Kacprzyk).


  1. 1.
    Butle, C.T., Rothstein, A.: On Conflict and Consensus: A Handbook on Formal Consensus Decision Making. Food Not Bombs Publishing, Takoma Park (2006)Google Scholar
  2. 2.
    Carlsson, C., Fedrizzi, M., Fuller, R.: Group decision support systems. In: Carlsson, C., Fedrizzi, M., Fuller, R. (eds.) Fuzzy Logic in Management, pp. 57–125. Springer Science, Berlin (2004)Google Scholar
  3. 3.
    Fedrizzi, M., Kacprzyk, J., Zadrożny, S.: An interactive multi-user decision support system for consensus reaching process using fuzzy logic with linguistic quantifiers. Decis. Support Syst. 4(3), 313–327 (1988)CrossRefzbMATHGoogle Scholar
  4. 4.
    Fedrizzi, M., Fedrizzi, M., Marques Pereira, R.A.: Consensus modelling in group decision making: a dynamical approach based on Zadeh’s fuzzy preferences. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds.) On Fuzziness (Homage to Lotfi A. Zadeh), pp. 165–170. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Gołuńska, D., Hołda, M.: The need of fairness in the group consensus reaching process in a fuzzy environment. Tech. Trans. Autom. Control 1–AC, 29–38 (2013)Google 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, pp. 1285–1290. Edmonton, Canada, 24–28 June 2013Google Scholar
  7. 7.
    Gołuńska, D., Kacprzyk, J., Zadrożny, S.: A consensus reaching support system based on concepts of ideal and anti-ideal point. In: Proceedings of the 2014 North American Fuzzy Information Processing Society Conference (NAFIPS 2014), pp. 1–6 (2014)Google Scholar
  8. 8.
    Gołuńska, D., Kacprzyk, J., Zadrożny, S.: A model of efficiency-oriented group decision and consensus reaching support system in a fuzzy environment. In: Proceedings of the 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU-2014, pp. 424–433 (2014)Google Scholar
  9. 9.
    Gołuńska, D., Kacprzyk, J., Zadrożny, S.: On efficiency-oriented support of consensus reaching in a group of agents in a fuzzy environment with a cost based preference updating approach. In: Proceedings of SSCI-2014. IEEE Press, Orlando (2014)Google Scholar
  10. 10.
    Gołuńska, D., Kacprzyk, J., Herrera-Viedma, E.: Modeling different advising attitudes in a consensus focused process of group decision making. In: Filev, D., et al. (ed.) Intelligent Systems’2014, Series: Advances in Intelligent Systems and Computing, vol. 322, pp. 279–288. Springer, Berlin (2015)Google Scholar
  11. 11.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Herrera-Viedma, E., García-Lapresta, J.L., Kacprzyk, J., Fedrizzi, M., Nurmi, H., Zadrożny, S. (eds.): Studies in fuzziness and soft computing. Consensual Processes. Springer, Berlin (2011)Google Scholar
  13. 13.
    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
  14. 14.
    Kacprzyk, J.: Group decision making with a fuzzy majority via linguistic quantifiers. Part I: a consensory like pooling. Cybern. Syst. Int. J. 16, 119–129. Part II: a competitive like pooling. Cybern. Syst. Int. J. 16, 131–144 (1985)Google Scholar
  15. 15.
    Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18(2), 105–118 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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
  17. 17.
    Kacprzyk, J., Fedrizzi, M.: A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. Eur. J. Oper. Res. 34, 315–325 (1988)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kacprzyk, J., Fedrizzi, M.: A ‘human-consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers. Math. Soc. Sci. 18, 275–290 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. Int. J. Gen. Syst. 30, 33–154 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Kacprzyk, J., Zadrożny, S.: On the use of fuzzy majority for supporting consensus reaching under fuzziness. In: Proceedings of FUZZ-IEEE’97 - Sixth IEEE International Conference on Fuzzy Systems (Barcelona, Spain), vol. 3, pp. 1683–1988 (1997)Google Scholar
  21. 21.
    Kacprzyk, J., Zadrożny, S.: An internet-based group decision and consensus reaching support system. Management 7(28), 4–10 (2003)Google Scholar
  22. 22.
    Kacprzyk, J., Zadrożny, S.: Supporting consensus reaching in a group via fuzzy linguistic data summaries. In: IFSA’2005 World Congress - Fuzzy Logic, Soft Computing and Computational Intelligence, pp. 1746–1751. Tsinghua University Press/Springer, Beijing (2005)Google Scholar
  23. 23.
    Kacprzyk, J., Zadrożny, S.: On a concept of a consensus reaching process support system based on the use of soft computing and Web techniques. In: Ruan, D., Montero, J., Lu, J., Martínez, L., D’hondt, P., Kerre, E.E. (eds.) Computational Intelligence in Decision and Control, pp. 859–864. World Scientific, Singapore (2008)Google Scholar
  24. 24.
    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. Int. J. Intell. Syst. 24(1), 4–26 (2009)CrossRefzbMATHGoogle Scholar
  25. 25.
    Kacprzyk, J., Zadrożny, S.: Soft computing and Web intelligence for supporting consensus reaching. Soft Comput. 14(8), 833–846 (2010)CrossRefGoogle Scholar
  26. 26.
    Kacprzyk, J., Zadrożny, S.: Supporting consensus reaching processes under fuzzy preferences and a fuzzy majority via linguistic summaries. In: Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R. (eds.) Preferences and Decisions, vol. 257, pp. 261–279 (2010)Google Scholar
  27. 27.
    Kacprzyk, J., Zadrożny, S.: Computing with words is an implementable paradigm: fuzzy queries, linguistic data summaries and natural language generation. IEEE Trans. Fuzzy Syst. 18(3), 461–472 (2010)CrossRefGoogle Scholar
  28. 28.
    Kacprzyk, J., Yager, R.R., Zadrożny, S.: A fuzzy logic based approach to linguistic summaries of databases. Int. J. Appl. Math. Comput. Sci. 10, 813–834 (2000)zbMATHGoogle Scholar
  29. 29.
    Kacprzyk, J., Zadrożny, S., Wilbik, A.: Linguistic summarization of some static and dynamic features of consensus reaching. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 19–28. Springer, Berlin (2006)CrossRefGoogle Scholar
  30. 30.
    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., Herrera, F., Montero, J. (eds.) Fuzzy Sets and Their Extensions: Representations, Aggregation and Models, pp. 263–295. Springer, Berlin (2008)CrossRefGoogle Scholar
  31. 31.
    Kacprzyk, J., Zadrożny, S., Raś, Z.W.: How to support consensus reaching using action rules: a novel approach. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 18(4), 451–470 (2010)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Loewer, B.: Special issue on consensus. Synthese 62, 1–122Google Scholar
  33. 33.
    Loewer, B., Laddaga, R.: Destroying the consensus. Synthese 62, 79–96 (1985)CrossRefGoogle Scholar
  34. 34.
    Perez, I.J., Wikström, R., Mezei, J., Carlsson, C., Anaya, K., Herrera-Viedma, E.: Linguistic consensus models based on a fuzzy ontology. Procedia Comput. Sci. 17, 498–505 (2013)CrossRefGoogle Scholar
  35. 35.
    Spillman, B., Spillman, R., Bezdek, J.C.: A fuzzy analysis of consensus in small groups. In: Wang, P.P., Chang, S.K. (eds.) Fuzzy Automata and Decision Processes, pp. 331–356. North-Holland, Amsterdam (1980)Google Scholar
  36. 36.
    Szmidt, E., Kacprzyk, J.: A consensus-reaching process under intuitionistic fuzzy preference relations. Int. J. Intell. Syst. 18(7), 837–852 (2003)CrossRefzbMATHGoogle Scholar
  37. 37.
    Turban, E., Aronson, J.E., Liang, T.P.: Decision Support Systems and Intelligent Systems, 6th edn. Prentice Hall, Upper Saddle River (2005)Google Scholar
  38. 38.
    Van de Walle, B., De Baets, B., Kerre, E.: A plea for the use of Lukasiewicz triplets in fuzzy preference structures. Part 1: general argumentation. Fuzzy Sets Syst. 97, 349–359 (1998)CrossRefzbMATHGoogle Scholar
  39. 39.
    Yager, R.R.: A new approach to the summarization of data. Inf. Sci. 28, 69–86 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Warszawa, KrakówPoland

Personalised recommendations