Theory and Decision

, Volume 52, Issue 4, pp 303–312 | Cite as

Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals

  • Gianni Bosi


It is well known that interval orders are particularly interesting in decision theory, since they are reflexive, complete and nontransitive binary relations which may be fully represented by means of two real-valued functions. In this paper, we discuss the existence of a pair of nonnegative, positively homogeneous and semicontinuous real-valued functionals representing an interval order on a real cone in a topological vector space. We recover as a particular case a result concerning the existence of a nonnegative, positively homogeneous and continuous utility functional for a complete preorder on a real cone in a topological vector space.

Interval order Topological vector space Utility function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bosi, G. (1998). A note on the existence of continuous representations of homothetic preferences on a topological vector space, Annals of Operations Research 80: 263–268.Google Scholar
  2. Bosi, G., Candeal, J.C. and Induráin, E. (2000). Continuous representability of homothetic preferences by means of homogeneous utility functions, Journal of Mathematical Economics 33: 291–298.Google Scholar
  3. Bridges, D.S. (1986). Numerical representation of interval orders on a topological space, Journal of Economic Theory 38: 160–166.Google Scholar
  4. Chateauneuf, A. (1987). Continuous representation of a preference relation on a connected topological space, Journal of Mathematical Economics 16: 139–146.Google Scholar
  5. Denneberg, D. (1994). Non-additive measure and integral, Kluwer Academic Publishers, Dordrecht.Google Scholar
  6. Dow, G. and Werlang, R.S. da C. (1992). Homothetic preferences, Journal of Mathematical Economics 21: 389–394.Google Scholar
  7. Fishburn, P.C. (1985). Interval orders and interval graphs, Wiley, New York.Google Scholar
  8. Oloriz, E., Candeal, J.C. and Induráin, E. (1998). Representability of interval orders, Journal of Economic Theory 78: 219–227.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Gianni Bosi
    • 1
  1. 1.Dipartimento di Matematica Applicata `Bruno de Finetti'Università di TriesteTriesteItaly

Personalised recommendations