Abstract
The R-greatest and maximal sets of standard choice theory are extended to fuzzy R-greatest and fuzzy maximal sets. Unlike the precise counterparts of these concepts, these two sets do not in general coincide when preferences are reflexive and connected. A stronger than usual version of connectedness under which the two sets are equal is provided. The concept of a fuzzy choice function is introduced and conditions under which a fuzzy choice function may be rationalized as a fuzzy R-greatest or a fuzzy maximal set are discussed. Rationalizability with transitive and weakly transitive fuzzy preference relations is also considered.
Similar content being viewed by others
References
Barrett CR, Pattanaik PK (1985) On vague preferences. In: H. von G. Enderle (ed) Ethik und Wirtschaftwissenschaft. Dunker & Humboldt, Berlin
Barrett CR, Pattanaik PK, Salles M (1986) On the structure of fuzzy social welfare functions. Fuzzy Sets Syst 19: 1–11
Barrett CR, Pattanaik PK, Salles M (1987) On choosing rationally when preferences are fuzzy. Mimeographed, Univ. of Birmingham, Birmingham, U.K.
Basu K (1984) Fuzzy revealed preference theory. J Econ Theory 32: 212–227
Dasgupta M, Deb R (1989) Transitivity and fuzzy preferences. Mimeographed, Dept. of Econ. SMU. Dallas, TX, USA
Deb R (1977) On Schwartz's Rule. J Econ Theory 16: 103–110
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York
Dutta B, Panda SC, Pattanaik PK (1986) Exact choice and fuzzy preferences. Math Soc Sci 11: 53–68
Kaufman A (1980) Introduction to theory of fuzzy subsets. Academic Press, New York
Nakamura K (1986) Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst 20: 147–162
Orlovsky SA (1978) Decision making with a fuzzy binary relation. Fuzzy Sets Syst 1: 155–167
Richter MK (1966) Revealed preference theory. Econometrica 34: 635–645
Roubens M (1989) Some properties of choice functions based on valued binary relations. Eur J Oper Res 40: 309–321
Sen AK (1970) Collective choice and social welfare. Oliver and Boyd, London
Sen AK (1971) Choice functions and revealed preference. Rev Econ Studies 38: 307–317
Świtalski Z (1988) Choice functions associated with fuzzy preference relations. In: Kacprzyk J, Roubens M (eds) Non-conventional preference relations in decision making (Lect. Notes Econ. Math. Systems, vol 301). Springer, Berlin Heidelberg New York
Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3: 177–200
Author information
Authors and Affiliations
Additional information
We are indebted to Professor P. K. Pattanaik for his comments on an earlier version of this paper. We also wish to acknowledge comments made by an anonymous referee from which this paper has benefited greatly. The usual caveat about errors applies.
Rights and permissions
About this article
Cite this article
Dasgupta, M., Deb, R. Fuzzy choice functions. Soc Choice Welfare 8, 171–182 (1991). https://doi.org/10.1007/BF00187373
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00187373