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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Arrow K.J. (1959). Rational choice functions and orderings. Economica 26, 121–127
Banerjee A. (1995). Fuzzy choice functions, revealed preference and rationality. Fuzzy Sets and Systems 70, 31–43
Barrett C.R., Pattanaik P.K., Salles M. (1986). On the Structure of fuzzy social welfare functions. Fuzzy Sets and Systems 19, 1–11
Barrett C.R., Pattanaik P.K., Salles M. (1990). On choosing rationally when preferences are fuzzy. Fuzzy Sets and Systems 34, 197–212
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
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
De Baets B., Mesiar R. (2002). Metrics and T-equalities. Journal of Mathematical Analysis and Applications 267, 531–547
De Wilde Ph. (2004). Fuzzy utility and equilibria. IEEE Transactions on Systems, Man and Cybernetics 34, 1774–1785
Dubois D., Prade H. (1980). Fuzzy sets and systems, theory and applications. New York, Academic Press
Fodor J., Roubens M. (1994). Fuzzy preference modelling and multicriteria decision support. Dordrecht, Kluwer
Georgescu I. (2004). On the axioms of revealed preference in fuzzy consumer theory. Journal of Systems Science and Systems Engineering 13, 279–296
Georgescu I. (2005a). Revealed preference, congruence and rationality: A fuzzy approach. Fundamenta Informaticae 65, 307–328
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
Georgescu I. (2007b). Arrow’s axiom and full rationality for fuzzy choice functions. Social Choice and Welfare 28, 303–319
Hájek, P. (1998). Methamathematics of fuzzy logic. Kluwer.
Hansson B. (1968). Choice structures and preference relations. Synthese 18, 443–458
Houthakker H.S. (1950). Revealed preference and utility functions. Economica 17, 159–174
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
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
Roubens M. (1989). Some properties of choice functions based on valued binary relations. European Journal of Operational Research 40, 309–321
Samuelson P.A. (1938). A note of the pure theory of consumer’s behavior. Economica 5, 61–71
Sen A.K. (1971). Choice functions and revealed preference. Review of Economic Studies 38, 307–317
Sen A.K. (1982). Choice, welfare and measurement. Cambridge, MA, MIT Press
Suzumura K. (1976). Rational choice and revealed preference. Review of Economic Studies 43, 149–159
Suzumura K. (1983). Rational choice, collective decisions and social welfare. Cambridge, Cambridge University Press
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
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
Zadeh L.A. (1971). Similarity relations and fuzzy orderings. Information Sciences 3, 177–200
Author information
Authors and Affiliations
Corresponding author
Rights 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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-007-9019-5