Skip to main content
Log in

Ranking fuzzy choice functions by their rationality indicators

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

In this paper we study two rationality indicators and two normality indicators of a fuzzy choice function. They express the degree of rationality or normality of this fuzzy choice function. This way we can establish a hierarchy in a given family of fuzzy choice functions with respect to their degree of rationality.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arrow K.J. (1959). Rational choice functions and orderings. Economica 26, 121–127

    Article  Google Scholar 

  • Banerjee A. (1995). Fuzzy choice functions, revealed preference and rationality. Fuzzy Sets and Systems 70, 31–43

    Article  MATH  MathSciNet  Google Scholar 

  • Barrett C.R., Pattanaik P.K., Salles M. (1986). On the Structure of fuzzy social welfare functions. Fuzzy Sets and Systems 19, 1–11

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Bělohlávek, R. (2002). Fuzzy relational systems. foundations and principles. Kluwer.

  • De Baets B., Fodor J. (1997). Twenty years of fuzzy preference relations (1978–1997). Belgian Journal of Operations Research, Statistics and Computer Science 37, 61–82

    MATH  MathSciNet  Google Scholar 

  • De Baets B., Mesiar R. (2002). Metrics and T-equalities. Journal of Mathematical Analysis and Applications 267, 531–547

    Article  MATH  MathSciNet  Google Scholar 

  • De Wilde Ph. (2004). Fuzzy utility and equilibria. IEEE Transactions on Systems, Man and Cybernetics 34, 1774–1785

    Article  Google Scholar 

  • Dubois D., Prade H. (1980). Fuzzy sets and systems, theory and applications. New York, Academic Press

    MATH  Google Scholar 

  • Fodor J., Roubens M. (1994). Fuzzy preference modelling and multicriteria decision support. Dordrecht, Kluwer

    MATH  Google Scholar 

  • Georgescu I. (2004). On the axioms of revealed preference in fuzzy consumer theory. Journal of Systems Science and Systems Engineering 13, 279–296

    Article  Google Scholar 

  • Georgescu I. (2005a). Revealed preference, congruence and rationality: A fuzzy approach. Fundamenta Informaticae 65, 307–328

    MATH  MathSciNet  Google Scholar 

  • Georgescu, I. (2005b). On the notion of dominance of fuzzy choice functions and its applications in multicriteria decision making. In L. Godo (Ed.), Symbolic and quantitative approaches to reasoning with uncertainty (Vol. 3571, pp. 257–268). Springer-Verlag, Lecture Notes in Artificial Intelligence Series.

  • Georgescu, I. (2005c). Rational choice and revealed preference: A fuzzy approach. PhD thesis, Turku Centre for Computer Science.

  • Georgescu I. (2007a). Similarity of fuzzy choice functions. Fuzzy Sets and Systems 158, 1314–1326

    Article  MATH  MathSciNet  Google Scholar 

  • Georgescu I. (2007b). Arrow’s axiom and full rationality for fuzzy choice functions. Social Choice and Welfare 28, 303–319

    Article  MathSciNet  Google Scholar 

  • Hájek, P. (1998). Methamathematics of fuzzy logic. Kluwer.

  • Hansson B. (1968). Choice structures and preference relations. Synthese 18, 443–458

    Article  MATH  Google Scholar 

  • Houthakker H.S. (1950). Revealed preference and utility functions. Economica 17, 159–174

    Article  MathSciNet  Google Scholar 

  • Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular norms. Kluwer.

  • Kulshreshtha P., Shekar B. (2000). Interrelationship among fuzzy Preference—based choice function and significance of rationality conditions: A taxonomic and intuitive perspective. Fuzzy Sets and Systems 109, 429–445

    Article  MATH  MathSciNet  Google Scholar 

  • Qiu, X, & Georgescu, I. (2005). Fuzzy choices support for agent–based automated negotiations. In CD-ROM Proceedings of the International Conference on Artificial Intelligence and Soft Computing IASTED 2005. Benidorm, Spain, September 2005.

  • Richter M. (1966). Revealed preference theory. Econometrica 34, 635–645

    Article  MATH  Google Scholar 

  • Roubens M. (1989). Some properties of choice functions based on valued binary relations. European Journal of Operational Research 40, 309–321

    Article  MATH  MathSciNet  Google Scholar 

  • Samuelson P.A. (1938). A note of the pure theory of consumer’s behavior. Economica 5, 61–71

    Article  Google Scholar 

  • Sen A.K. (1971). Choice functions and revealed preference. Review of Economic Studies 38, 307–317

    Article  MATH  Google Scholar 

  • Sen A.K. (1982). Choice, welfare and measurement. Cambridge, MA, MIT Press

    MATH  Google Scholar 

  • Suzumura K. (1976). Rational choice and revealed preference. Review of Economic Studies 43, 149–159

    Article  MATH  Google Scholar 

  • Suzumura K. (1983). Rational choice, collective decisions and social welfare. Cambridge, Cambridge University Press

    Google Scholar 

  • Turunen, T. (1999). Mathematics behind fuzzy Logic. Physica-Verlag.

  • Uzawa H. (1956). A note on preference and axioms of choice. Annals of the Institute of Statistical Mathematics 8, 35–40

    Article  MATH  MathSciNet  Google Scholar 

  • Uzawa H. (1959). Preference and rational choice in the theory of consumption. In: Arrow K.J., Karlin S., Suppes P.(eds) Mathematical methods in the social sciences. Stanford, Stanford University Press

    Google Scholar 

  • Zadeh L.A. (1971). Similarity relations and fuzzy orderings. Information Sciences 3, 177–200

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Irina Georgescu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgescu, I. Ranking fuzzy choice functions by their rationality indicators. Fuzzy Optim Decis Making 6, 367–389 (2007). https://doi.org/10.1007/s10700-007-9019-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-007-9019-5

Keywords

Navigation