Skip to main content

OWA Operators in Group Decision Making and Consensus Reaching Under Fuzzy Preferences and Fuzzy Majority

  • Chapter
The Ordered Weighted Averaging Operators

Abstract

We discuss the use of Yager’s (1988) ordered weighted averaging (OWA) operators with importance qualification (Yager, 1993, 1996) for dealing with a fuzzy majority, meant as a linguistic quantifier (most, almost all, … ), in group decision making and consensus formation under fuzzy preferences. We show how new solution concepts in group decision making, and new “soft” degrees of consensus can be defined.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Barrett, C.R., Pattanaik, P.K. and Salles, M. (1990). On choosing rationally when preferences are fuzzy. Fuzzy Sets and Systems, 34, 197–212.

    Article  MathSciNet  MATH  Google Scholar 

  • Barrett, C.R., Pattanaik, P.K. and Salles, M. (1992). Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets and Systems, 49, 9–13.

    Article  MathSciNet  MATH  Google Scholar 

  • Bezdek, J.C., Spillman, B. Spillman, R. (1978). A fuzzy relation space for group decision theory, Fuzzy Sets and Systems, 1, 255–268.

    Article  MathSciNet  MATH  Google Scholar 

  • Blin, J.M. (1974). Fuzzy relations in group decision theory, Journal of Cybernetics, 4, 17–22.

    Article  Google Scholar 

  • Blin, J.M. and Whinston, A.P. (1973). Fuzzy sets and social choice, Journal of Cybernetics, 4, 17–22.

    Article  Google Scholar 

  • Carlsson, Ch. et al. (1992). Consensus in distributed soft environments, European Journal of Operational Research, 61, 165–185.

    Article  Google Scholar 

  • Delgado, M., Verdegay, J.L. and Vila, M.A. (1993). On aggregation operations of linguistic labels, International Journal of Intelligent Systems, 8, 351–370.

    Article  MATH  Google Scholar 

  • Fedrizzi, M. and Kacprzyk, J. (1988). On measuring consensus in the setting of fuzzy preference relations. In J. Kacprzyk and M. Roubens (Eds.): Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Berlin, pp. 129–141.

    Google Scholar 

  • Fedrizzi, M. and Kacprzyk, J. (1993). Consensus degrees under fuzzy majorities and preferences using OWA (ordered weighted average) operators, Proceedings of Fifth IFSA World Congress’ 93 (Seoul, Korea), Vol. I, pp. 624–626.

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1996). How different are social choice functions: a rough sets approach, Quality and Quantity, 30, 87–99.

    Google Scholar 

  • Fedrizzi, M., Kacprzyk, J., Owsinski, J.W. and Zadrozny, S. (1994). Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles, Annals of Operations Research, 51, 127–139.

    Article  MATH  Google Scholar 

  • Fedrizzi, M., Kacprzyk, J. and Zadrozny, S. (1988). An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers, Decision Support Systems, 4, 313–327.

    Article  Google Scholar 

  • Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1996). A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78, 73–88.

    Article  MathSciNet  Google Scholar 

  • Kacprzyk, J. (1984). Collective decision making with a fuzzy majority rule, Proc. WOGSC Congress, AFCET, Paris, pp. 153–159.

    Google Scholar 

  • Kacprzyk, J. (1985a). Zadeh’s commonsense knowledge and its use in multi-criteria, multistage and multiperson decision making. In M.M. Gupta et al. (Eds.): Approximate Reasoning in Expert Systems, North-Holland, Amsterdam, pp. 105–121.

    Google Scholar 

  • Kacprzyk, J. (1985b). Group decision-making with a fuzzy majority via linguistic quantifiers. Part I: A consensory-like pooling; Part II: A competitive-like pooling, Cybernetics and Systems: an International Journal, 16, 119–129 (Part I), 131-144 (Part II).

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. (1987a). On some fuzzy cores and’ soft ‘consensus measures in group decision making. In J.C. Bezdek (Ed.): The Analysis of Fuzzy Information, Vol. 2, CRC Press, Boca Raton, pp. 119–130.

    Google Scholar 

  • Kacprzyk, J. (1987b). Towards’ human consistent ‘decision support systems through commonsense-knowledge-based decision making and control models: a fuzzy logic approach, Computers and Artificial Intelligence, 6, 97–122.

    MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1986). “Soft” consensus measures for monitoring real consensus reaching processes under fuzzy preferences, Control and Cybernetics, 15, 309–323.

    MathSciNet  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1988). A “soft” measure of consensus in the setting of partial (fuzzy) preferences, European Journal of Operational Research, 34, 315–325.

    Article  MathSciNet  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1989). A “human-consistent” degree of consensus based on fuzzy logic with linguistic quantifiers, Mathematical Social Sciences, 18, 275–290.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M., Eds. (1990). Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, ordrecht.

    MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1995). Consensus degrees under fuzziness via ordered weighted average (OWA) operators. In Z. Bien and K.C. Min (Eds.): Fuzzy Logic and its Applications in Engineering, Information Sciences and Intelligent Systems, Kluwer, Dordrecht, pp. 447–454.

    Chapter  Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1990). Group decision making with fuzzy majorities represented by linguistic quantifiers. In J.L. Verde-gay and M. Delgado (Eds.): Approximate Reasoning Tools for Artificial Intelligence, Verlag TÜV Rheinland, Cologne, pp. 126–145.

    Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1992a). Fuzzy logic with linguistic quantifiers in group decision making and consensus formation. In R.R. Yager and L.A. Zadeh (Eds.): An Introduction to Fuzzy Logic Applications in Intelligent Systems, Kluwer, Dordrecht, 263–280.

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J., Nurmi, H. and Fedrizzi, M., Eds. (1997). Consensus under Fuzziness, Kluwer, Boston.

    MATH  Google Scholar 

  • Kacprzyk, J. and Roubens, M., Eds. (1988). Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Heidelberg.

    MATH  Google Scholar 

  • Loewer, B. and Laddaga, R. (1985). Destroying the consensus, in Loewer B., Guest Ed., Special Issue on Consensus, Synthese, 62(1), pp. 79–96.

    Google Scholar 

  • Nurmi, H. (1981). Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249–259.

    Article  MathSciNet  MATH  Google Scholar 

  • Nurmi, H. (1987). Comparing Voting Systems, Reidel, Dordrecht.

    Book  Google Scholar 

  • Nurmi, H. (1988). Assumptions on individual preferences in the theory of voting procedures. In J. Kacprzyk and M. Roubens (Eds.): Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Heidelberg, pp. 142–155.

    Google Scholar 

  • Nurmi, H., Fedrizzi, M. and Kacprzyk, J. (1990). Vague notions in the theory of voting. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 43–52.

    Chapter  Google Scholar 

  • Nurmi, H. and Kacprzyk, J. (1991). On fuzzy tournaments and their solution concepts in group decision making, European Journal of Operational Research, 51, 223–232.

    Article  MATH  Google Scholar 

  • Nurmi H., Kacprzyk, J. and Fedrizzi, M. (1996). Probabilistic, fuzzy and rough concepts in social choice, European Journal of Operational Research, 95, 264–277.

    Article  MATH  Google Scholar 

  • Tanino, T. (1990). On group decision making under fuzzy preferences. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 172–185.

    Chapter  Google Scholar 

  • Torra, V. (1997) The weighted OWA operator, International Journal of Intelligent Systems, 12, 151–166.

    Article  Google Scholar 

  • Yager, R.R (1988). On ordered weighted averaging aggregation operators in-multicriteria decisionmaking, IEEE Trans. on Systems, Man and Cybernetics, SMC-18, 183–190.

    Article  MathSciNet  Google Scholar 

  • Yager, R.R. (1993). On the Issue of Importance Qualifications in Fuzzy Multi-Criteria Decision Making. Tech. Report MII-1323, Machine Intelligence Institute, Iona College, New Rochelle, NY.

    Google Scholar 

  • Yager, R.R. (1996). Quantifier quided aggregation using OWA operators, International Journal of Intelligent Systems, 11, 49–73.

    Article  Google Scholar 

  • Zadeh, L.A. (1983). A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications, 9, 149–184.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kacprzyk, J., Fedrizzi, M., Nurmi, H. (1997). OWA Operators in Group Decision Making and Consensus Reaching Under Fuzzy Preferences and Fuzzy Majority. In: Yager, R.R., Kacprzyk, J. (eds) The Ordered Weighted Averaging Operators. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6123-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-6123-1_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7806-8

  • Online ISBN: 978-1-4615-6123-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics