Skip to main content
SpringerLink
Log in

Towards a Fairness-Oriented Approach to Consensus Reaching Support Under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries

  • Chapter
  • First Online:
Transactions on Computational Collective Intelligence XXIII

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 9760))

Abstract

A novel approach to a human centric support of a consensus reaching process in a group of agents who present their testimonies as individual fuzzy preference relations is proposed. The concept of a degree of consensus is used which is meant as the degree to which, for instance, most of important agents agree as to almost all of relevant options. The fuzzy majorities are equated with linguistic quantifiers and Zadeh’s calculus of linguistically quantified propositions is used. The new concepts of a consensory and dissensory agent is introduced. The authors’ approach of using linguistic data summaries for a comprehensive summarization of how the agents’ current testimonies look like is then employed for the consensory and dissensory agents to obtain suggestions to the agents on changes of specific preferences that could lead to a higher degree of consensus. An explicit inclusion of opinions of the consensory and dissensory agents is shown to be an important step towards a fairness type attitude of the moderator as opinions of all agents are accounted for.

Partially supported by the National Science Centre under Grant UMO-2012/05/B/ST6/03068.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chatterjee, S.: Reaching a consensus: some limit theorems. Proc. Int. Statist. Inst., 159–164 (1975)

    Google Scholar 

  2. Chatterjee, S., Seneta, E.: Toward consensus: some convergence theorems on repeated averaging. J. Appl. Probab. 14, 89–97 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  3. Choi, S.-S., Cha, S.-H., Tappert, C.C.: A survey of binary similarity and distance measures. J. Syst. Cybern. Inform. 8(1), 43–48 (2010)

    Google Scholar 

  4. De Groot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69, 118–121 (1974)

    Article  MATH  Google Scholar 

  5. Delgado, M., Ruiz, M.D., Sánchez, D., Vila, M.A.: Fuzzy quantification: a state of the art. Fuzzy Sets Syst. 242, 1–30 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fedrizzi, M., Kacprzyk, J., Nurmi, H.: Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators. Control Cybern. 22, 71–80 (1993)

    MathSciNet  MATH  Google Scholar 

  7. Fedrizzi, M., Kacprzyk, J., Owsińnski, J.W., Zadrożny, S.: Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles. Ann. Oper. Res. 51, 127–139 (1994)

    Article  MATH  Google Scholar 

  8. Fedrizzi, M., Kacprzyk, J., Zadrożny, S.: An interactive multi - user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers. Decis. Support Syst. 4, 313–327 (1988)

    Article  MATH  Google Scholar 

  9. 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 

  10. Gołuńska, D., Kacprzyk, J.: The conceptual framework of fairness in consensus reaching process under fuzziness. In: Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, pp. 1285–1290. Edmonton, Canada (2013a)

    Google Scholar 

  11. Gołuńska, D., Kacprzyk, J., Herrera-Viedma, E.: Modeling different advising attitudes in a consensus focused process of group decision making. In: Angelov, P., et al. (eds.) Intelligent Systems 2014. AISC, vol. 322, 1st edn, pp. 279–288. Springer, Heidelberg (2013)

    Google Scholar 

  12. Gołuńska, J., Kacprzyk, S. Zadrożny : 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 

  13. Gołuńska, D., Kacprzyk, J., Zadrożny, S.: A new model of efficiency-oriented group decision and consensus reaching support system in a fuzzy environment. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Communications in Computer and Information Science, vol. 443, pp. 424–433. Springer, Heidelberg (2014a)

    Google Scholar 

  14. Gołuńska, J., Kacprzyk, S.Zadrożny: 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: 2014 IEEE Symposium Series on Computational Intelligence, pp. 15–21. IEEE Press, Orlando, USA (2014b)

    Google Scholar 

  15. Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence: models, analysis, and simulation. J. Artif. Soc. Soc. Simul. 5(3), 1–33 (2002). http://jasss.soc.surrey.ac.uk/5/3/2.html

    Google Scholar 

  16. Herrera-Viedma, E., Cabrerizo, F., Kacprzyk, J., Pedrycz, W.: A review of soft consensus models in a fuzzy environment. Inf. Fusion 17, 4–13 (2014)

    Article  Google Scholar 

  17. Kacprzyk, J.: Group decision - making with a fuzzy majority via linguistic quantifiers. Part I: a consensory - like pooling; Part II: a competitive - like pooling. Cybern. Syst. Int. J. 16, 119–129 (Part I), 131–144 (Part II) (1985)

    Google Scholar 

  18. Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18, 105–118 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kacprzyk, J., Fedrizzi, M.: ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control Cybern. 15, 309–323 (1986)

    MathSciNet  MATH  Google Scholar 

  20. Kacprzyk, J., Fedrizzi, M.: A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. Eur. J. Oper. Res. 34, 315–325 (1988)

    Article  MathSciNet  Google Scholar 

  21. Kacprzyk, J., Fedrizzi, M.: A ‘human - consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers. Math. Soc. Sci. 18, 275–290 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kacprzyk, J., Fedrizzi, M. (eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory. Kluwer, Dordrecht (1990)

    MATH  Google Scholar 

  23. Kacprzyk, J., Nurmi, H.: On fuzzy tournaments and their solution concepts in group decision making. Eur. J. Oper. Res. 51, 223–232 (1991)

    Article  MATH  Google Scholar 

  24. Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Syst. 49, 21–31 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summarization of time series using a fuzzy quantifier driven aggregation. Fuzzy Sets and Syst. 159(12), 1485–1499 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. Int. J. Gen. Syst. 30(2001), 33–154 (2001)

    MathSciNet  MATH  Google Scholar 

  27. 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)

    MATH  Google Scholar 

  28. Kacprzyk, J., Zadrożny, S.: Computing with words in decision making through individual and collective linguistic choice rules. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 9, 89–102 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kacprzyk, J., Zadrożny, S.: Computing with words in decision making through individual and collective linguistic choice rules. Int. J. Uncertainty, Fuzziness Knowl. Based Syst. 9, 89–102 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kacprzyk, J., Zadrożny, S.: Collective choice rules in group decision making under fuzzy preferences and fuzzy majority: a unified OWA operator based approach. Control Cybern. 31, 937–948 (2002)

    MATH  Google Scholar 

  31. Kacprzyk, J., Zadrożny, S.: Dealing with imprecise knowledge on preferences and majority in group decision making: towards a unified characterization of individual and collective choice functions. Bull. Pol. Acad. Sci. (Tech. Sci.) 51, 279–302 (2003)

    MATH  Google Scholar 

  32. Kacprzyk, J., Zadrożny, S.: An internet-based group decision support system. Management VII(28), 4–10 (2003)

    Google Scholar 

  33. Kacprzyk, J., Zadrożny, S.: Linguistic database summaries and their protoforms: towards natural language based knowledge discovery tools. Inf. Sci. 173(4), 281–304 (2005)

    Article  MathSciNet  Google Scholar 

  34. 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)

    Chapter  Google Scholar 

  35. 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)

    Article  MATH  Google Scholar 

  36. Kacprzyk, J., Zadrożny, S.: Protoforms of linguistic database summaries as a human consistent tool for using natural language in data mining. Int. J. Softw. Sci. Comput. Intell. 1(1), 100–111 (2009)

    Article  Google Scholar 

  37. Kacprzyk, J., Zadrożny, S.: Soft computing and Web intelligence for supporting consensus reaching. Soft Comput. 14(8), 833–846 (2010a)

    Article  Google Scholar 

  38. 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 (2010b)

    Article  Google Scholar 

  39. Kacprzyk, J., Zadrożny, S.: Modern data-driven decision support systems: the role of computing with words and computational linguistics. Int. J. Gen. Syst. 39(4), 379–393 (2010c)

    Article  MATH  Google Scholar 

  40. Kacprzyk, J., Zadrożny, S.: Supporting consensus reaching processes under fuzzy preferences and a fuzzy majority via linguistic summaries. In: Greco, S., Pereira, R.A.M., Squillante, M., Yager, R.R., Kacprzyk, J. (eds.) Preferences and Decisions. STUDFUZZ, vol. 257, pp. 261–279. Springer, Heidelberg (2010d)

    Chapter  Google Scholar 

  41. Kacprzyk, J., Zadrożny, S.: Comprehensiveness of linguistic data summaries: a crucial role of protoforms. In: Moewes, C., Nürnberger, A. (eds.) Computational Intelligence in Intelligent Data Analysis. SCI, vol. 445, pp. 207–221. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  42. 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 a granulation perspective. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 906–929. Wiley, Chichester (2008)

    Google Scholar 

  43. Kacprzyk, J., Zadrożny, S., Raś, Z.: Action rules in consensus reaching process support. Proceedings of ISDA’2009 - The 9th International Conference on Intelligent Systems Design and Applications, pp. 827–832. IEEE Press, Pisa (2009)

    Chapter  Google Scholar 

  44. Kacprzyk, J., Zadrożny, S., Raś, Z.W.: How to support consensus reaching using action rules: a novel approach. Int. J. Uncertainty, Fuzziness Knowl. Based Syst. 18(4), 451–470 (2010)

    Article  MathSciNet  Google Scholar 

  45. 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, Heidelberg (2006)

    Chapter  Google Scholar 

  46. Krause, U.: A discrete nonlinear and non-autonomous model of consensus formation. In: Elaydi, S., Ladas, G., Popenda, J., Rakowski, J. (eds.) Communications in Difference Equations, pp. 227–236. Gordon and Breach, Amsterdam (2000)

    Google Scholar 

  47. Loewer, B., Laddaga, R.: Destroying the consensus. Synthese 62(1), 79–96 (1985). Loewer B., Guest (ed.) Special Issue on Consensus

    Article  Google Scholar 

  48. Nurmi, H.: Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets Syst. 6, 187–198 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  49. Reiter, E., Dale, R.: Building Natural Language Generation Systems. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  50. Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in group decision making. Notes Intuitionistic Fuzzy Sets 2, 15–32 (1996)

    MathSciNet  MATH  Google Scholar 

  51. Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy relations and consensus formations. Notes Intuitionistic Fuzzy Sets 6, 1–10 (2000)

    MathSciNet  Google Scholar 

  52. Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Control Cybern. 31, 1055–1057 (2002)

    MATH  Google Scholar 

  53. Szmidt, E., Kacprzyk, J.: A consensus-reaching process under intuitionistic fuzzy preference relations. Int. J. Intell. Syst. 18(7), 837–852 (2003)

    Article  MATH  Google Scholar 

  54. Yager, R.R.: A new approach to the summarization of data. Inf. Sci. 28, 69–86 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  55. Yager, R.R.: On ordered weighted averaging operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. SMC–18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  56. Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer, Boston (1997)

    Google Scholar 

  57. Yager, R.R., Kacprzyk, J., Beliakov, G. (eds.): Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Springer, Heidelberg (2011)

    Google Scholar 

  58. Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  59. Zadrożny, S.: An approach to the consensus reaching support in fuzzy environment. In: Kacprzyk, J., Nurmi, H., Fedrizzi, M. (eds.) Consensus under Fuzziness, pp. 83–109. Kluwer, Boston (1997)

    Chapter  Google Scholar 

  60. Zadrożny, S., Furlani, P.: Modelling and supporting of the consensus reaching process using fuzzy preference relations. Control Cybern. 20, 135–154 (1991)

    Google Scholar 

  61. Zadrożny, S., Kacprzyk, J.: An internet-based group decision and consensus reaching support system. In: Yu, X., Kacprzyk, J. (eds.) Applied Decision Support with Soft Computing, pp. 263–275. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk & Sławomir Zadrożny

Authors
  1. Janusz Kacprzyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sławomir Zadrożny
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Janusz Kacprzyk .

Editor information

Editors and Affiliations

  1. Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, Australia

    Ryszard Kowalczyk

  3. WSB University in Wroclaw, Wroclaw, Poland

    Jacek Mercik

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kacprzyk, J., Zadrożny, S. (2016). Towards a Fairness-Oriented Approach to Consensus Reaching Support Under Fuzzy Preferences and a Fuzzy Majority via Linguistic Summaries. In: Nguyen, N., Kowalczyk, R., Mercik, J. (eds) Transactions on Computational Collective Intelligence XXIII. Lecture Notes in Computer Science(), vol 9760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52886-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-52886-0_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-52885-3

  • Online ISBN: 978-3-662-52886-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation