Skip to main content

On the Notion of Dominance of Fuzzy Choice Functions and Its Application in Multicriteria Decision Making

  • Conference paper
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3571))

Abstract

The aim of this paper is twofold: The first objective is to study the degree of dominance of fuzzy choice functions, a notion that generalizes Banerjee’s concept of dominance. The second objective is to use the degree of dominance as a tool for solving multicriteria decision making problems. These types of problems describe concrete economic situations where partial information or human subjectivity appears. The mathematical modelling is done by formulating fuzzy choice problems where criteria are represented by fuzzy available sets of alternatives.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow, K.J.: Rational Choice Functions and Orderings. Economica 26, 121–127 (1959)

    Article  Google Scholar 

  2. Banerjee, A.: Fuzzy Choice Functions, Revealed Preference and Rationality. Fuzzy Sets Syst. 70, 31–43 (1995)

    Article  MATH  Google Scholar 

  3. Barrett, C.R., Pattanaik, P.K., Salles, M.: On the Structure of Fuzzy Social Welfare Functions. Fuzzy Sets Syst. 19, 1–11 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Barrett, C.R., Pattanaik, P.K., Salles, M.: On Choosing Rationally When Preferences Are Fuzzy. Fuzzy Sets Syst. 34, 197–212 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barrett, C.R., Pattanaik, P.K., Salles, M.: Rationality and Aggregation of Preferences in an Ordinal Fuzzy Framework. Fuzzy Sets Syst. 49, 9–13 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bělohlávek, R.: Fuzzy Relational Systems. Foundations and Principles. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  7. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  8. Georgescu, I.: On the Axioms of Revealed Preference in Fuzzy Consumer Theory. J. Syst. Science Syst. Eng. 13, 279–296 (2004)

    Article  Google Scholar 

  9. Georgescu, I.: Revealed Preference, Congruence and Rationality. Fund. Inf. 65, 307–328 (2005)

    MATH  MathSciNet  Google Scholar 

  10. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  11. Kulshreshtha, P., Shekar, B.: Interrelationship among Fuzzy Preference - based Choice Function and Significance of Rationality Conditions: a Taxonomic and Intuitive Perspective. Fuzzy Sets Syst 109, 429–445 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Richter, M.: Revealed Preference Theory. Econometrica 34, 635–645 (1966)

    Article  MATH  Google Scholar 

  13. Richter, M.: Rational Choice. In: Chipman, J.S. et al. (eds.): Preference, Utility, and Demand. Harcourt Brace Jovanovich, New-York (1971)

    Google Scholar 

  14. Samuelson, P.A.: A Note on the Pure Theory of Consumers’ Behaviour. Economica 5, 61–71 (1938)

    Article  Google Scholar 

  15. Sen, A.K.: Choice Functions and Revealed Preference. Rev. Ec. Studies 38, 307–312 (1971)

    Article  MATH  Google Scholar 

  16. De Wilde, P.: Fuzzy Utility and Equilibria. IEEE Trans. Syst., Man and Cyb. 34, 1774–1785 (2004)

    Article  Google Scholar 

  17. Wang, X.: A Note on Congruous Conditions of Fuzzy Choice Functions. Fuzzy Sets Syst. 145, 355–358 (2004)

    Article  MATH  Google Scholar 

  18. Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill, New York (1982)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Georgescu, I. (2005). On the Notion of Dominance of Fuzzy Choice Functions and Its Application in Multicriteria Decision Making. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_23

Download citation

  • DOI: https://doi.org/10.1007/11518655_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27326-4

  • Online ISBN: 978-3-540-31888-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics