Continuous representability of interval orders

Authors

  • Juan C. Candeal Universidad de Zaragoza
  • Esteban Induráin Universidad Pública de Navarra
  • M. Zudaire Instituto de Educación Secundaria Barañain

DOI:

https://doi.org/10.4995/agt.2004.1971

Keywords:

Orderings on a set, Interval orders, Numerical representations of orderings, Continuous representations of orderings

Abstract

In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order, and its representability through a pair of continuous real-valued functions. Inspired in recent characterizations of the representability of interval orders, we obtain new results concerning the existence of continuous real-valued representations. Classical results are also restated in a unified framework.

Downloads

Download data is not yet available.

Author Biographies

Juan C. Candeal, Universidad de Zaragoza

Departamento de Análisis Económico

Esteban Induráin, Universidad Pública de Navarra

Departamento de Matemática e Informática

References

J. Aczél and J. Dhombres, Functional equations in several variables, Cambridge University Press. (Cambridge, U.K. 1991).

G. Birkhoff, Lattice theory, (Third edition). American Mathematical Society. (Providence, RI. 1967).

G. Bosi , J. C. Candeal , E. Induráin, E. Olóriz and M. Zudaire, Numerical representations of interval orders, Order 18 (2001), 171-190. http://dx.doi.org/10.1023/A:1011974420295

G. Bosi and R. Isler, Representing preferences with nontransitive indifference by a single real-valued function, Journal of Mathematical Economics 24 (1995), 621-631. http://dx.doi.org/10.1016/0304-4068(94)00706-G

Bridges D. S., Representing interval orders by a single real-valued function, Journal of Economic Theory 36 (1985), 149-155. http://dx.doi.org/10.1016/0022-0531(85)90083-3

D. S. Bridges and G. B.Mehta, Representations of preference orderings, Springer-Verlag. (Berlin. 1995). http://dx.doi.org/10.1007/978-3-642-51495-1

J. C. Candeal and E. Induráin, Sobre caracterizaciones topológicas de la representabilidad de cadenas mediante funciones de utilidad, Revista Española de Economía 7 (2) (1990), 235-244.

J. C. Candeal and E. Induráin, Utility functions on chains, Journal of Mathematical Economics 22 (1993), 161-168. http://dx.doi.org/10.1016/0304-4068(93)90045-M

J. C. Candeal and E. Induráin, Lexicographic behaviour of chains, Archiv der Mathematik 72 (1999), 145-152. http://dx.doi.org/10.1007/s000130050315

J. C. Candeal and E. Induráin, and M. Zudaire, Numerical representability of semiorders, Mathematical Social Sciences 43 (2002), 61-77. http://dx.doi.org/10.1016/S0165-4896(01)00082-8

A. Chateauneuf, Continuous representation of a preference relation on a connected topological space, Journal of Mathematical Economics 16 (1987), 139-146. http://dx.doi.org/10.1016/0304-4068(87)90003-6

G. Debreu, Representation of a preference ordering by a numerical function, In Decision processes, edited by R. Thrall, C. Coombs and R. Davies. John Wiley. (New York. 1954).

G. Debreu, Continuity properties of Paretian utility, International Economic Review 5 (1964), 285-293. http://dx.doi.org/10.2307/2525513

J. P. Doignon, A. Ducamp and J. C. Falmagne, On realizable biorders and the biorder dimension of a relation, Journal of Mathematical Psychology 28 (1984), 73-109. http://dx.doi.org/10.1016/0022-2496(84)90020-8

J. Dugundji, Topology, Allyn and Bacon. (Boston. 1966).

S. Eilenberg, Ordered topological spaces, American Journal of Mathematics 63 (1941), 39-45. http://dx.doi.org/10.2307/2371274

P. C. Fishburn, Intransitive indifference with unequal indifference intervals, Journal of Mathematical Psychology 7 (1970), 144-149. http://dx.doi.org/10.1016/0022-2496(70)90062-3

P. C. Fishburn, Intransitive indifference in preference theory: a survey, Operations Research 18 (2) (1970), 207-228. http://dx.doi.org/10.1287/opre.18.2.207

P. C. Fishburn, Utility theory for decision-making, Wiley, (New York. 1970).

P. C. Fishburn, Interval representations for interval orders and semiorders, Journal of Mathematical Psychology 10 (1973), 91-105. http://dx.doi.org/10.1016/0022-2496(73)90007-2

P. C. Fishburn, Interval orders and interval graphs, (Wiley, New York. 1985).

S. H. Gensemer, On numerical representations of semiorders, Discussion Paper n. 5. Department of Economics. University of Syracuse, (N.Y. 1986).

S. H. Gensemer, On relationships between numerical representations of interval orders and semiorders, Journal of Economic Theory 43 (1987), 157-169. http://dx.doi.org/10.1016/0022-0531(87)90119-0

S. H. Gensemer, Continuous semiorder representations, Journal of Mathematical Economics 16 (1987), 275-289. http://dx.doi.org/10.1016/0304-4068(87)90013-9

S. H. Gensemer, On numerical representations of semiorders, Mathematical Social Sciences 15 (3) (1988), 277-286. http://dx.doi.org/10.1016/0165-4896(88)90012-1

L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag. (New York. 1960). http://dx.doi.org/10.1007/978-1-4615-7819-2

E. Olóriz, J. C. Candeal and E. Induráin, Representability of interval orders, Journal of Economic Theory 78 (1) (1998), 219-227. http://dx.doi.org/10.1006/jeth.1997.2346

Downloads

How to Cite

[1]
J. C. Candeal, E. Induráin, and M. Zudaire, “Continuous representability of interval orders”, Appl. Gen. Topol., vol. 5, no. 2, pp. 213–230, Oct. 2004.

Issue

Section

Articles