Skip to main content

Single-Peakedness in Weighted Aggregation of Fuzzy Opinions in a Fuzzy Group

  • Chapter

Part of the book series: Theory and Decision Library ((TDLB,volume 18))

Abstract

In this paper it is considered a formal approach to the problem of aggregating individual opinions in a fuzzy group, when alternatives can be represented in a real hyper-space and each individual defines his/her fuzzy set of non rejectable alternatives. On one hand, weighted aggregation rule for consensus opinion is axiomatically justified. On the other hand, it is shown a sufficient condition for the stability of such consensus solution.

Research supported by Dirección General de Investigación Cientifica y Técnica (National Grant number PB88-0137)

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • K.J. Arrow ( 1951, 1964), Social Choice and Individual Values, Wiley, New York.

    Google Scholar 

  • D. Black (1958), The Theory of Committees and Elections, Cambridge University Press, Cambridge.

    Google Scholar 

  • W. Cholewa (1985), Aggregation of Fuzzy Opinions: an Axiomatic Approach, Fuzzy Sets Syst. 17, 249–258.

    Article  Google Scholar 

  • D. Dubois and J.L. Koning (1989), Social Choice Axioms forFuzzy Sets Aggregation,Fuzzy Sets Syst. (to appear).

    Google Scholar 

  • D. Dubois and H. Prade (1985), A review of Fuzzy sets Aggregation Connectives, Inf. Sci. 36, 85–121.

    Article  Google Scholar 

  • L.W. Fung and K.S. Fu (1975), An Axiomatic Approach to Rational Decision Making in a Fuzzy Environment; in: L.A. Zadeh, K.S. Fu, K. Tanaka and M. Shimura (Eds.), Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, pp. 227–256.

    Google Scholar 

  • K. Inada (1964), A Note on Simple Majority Rule, Econometrica 32, 525–531.

    Article  Google Scholar 

  • J. Montero (1985), A note on Fung-Fu’s Theorem, Fuzzy Sets Syst. 17, 259–269.

    Article  Google Scholar 

  • J. Montero (1988a), Aggregation of Fuzzy Opinions in a Non-Homogeneous Group, Fuzzy Sets Syst. 25, 15–20.

    Article  Google Scholar 

  • J. Montero (1988b), An Axiomatic Approach to Fuzzy Multicriteria Analysis; in: M.M. Gupta and T. Yamakawa (Eds.), Fuzzy Logic in Knowledge-Based Systems, Decision and Control, North-Holland, Amsterdam, pp. 259–269.

    Google Scholar 

  • J. Montero (1989), Weighted Aggregation and Single Peaked Intensities, Workshop on Aggregation and Best Choices on Imprecise Opinions, Brussels.

    Google Scholar 

  • P.K. Pattanaik (1971), Voting and Collective Choice, Cambridge University Press, Cambridge.

    Google Scholar 

  • A.K. Sen (1970), Collective Choice and Social Welfare, Holden-Day, San Francisco.

    Google Scholar 

  • J.C. Vansnick (1987), Intensity of Preference; in: Y. Sawaragi, K. Inoue and H. Nakayama (Eds.), Toward Interactive and Intelligent Decision Support Systems (Volume 2), Springer-Verlag, Berlin, pp. 220–229.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Kluwer Academic Publishers

About this chapter

Cite this chapter

Montero, J. (1990). Single-Peakedness in Weighted Aggregation of Fuzzy Opinions in a Fuzzy Group. In: Kacprzyk, J., Fedrizzi, M. (eds) Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory. Theory and Decision Library, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2109-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2109-2_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7448-3

  • Online ISBN: 978-94-009-2109-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics