Continuous representation of interval orders by means of decreasing scales

Matematicki Vesnik

Volumn 58, Issue 3-4, 2006, Pages 111-117

  Bosi, Gianni ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Continuous numerical representation; Decreasing scale; Interval order

Indexed keywords

EID: 33845740622     PISSN: 00255165     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. J.C.R. Alcantud, G. Bosi, M.J. Campión, J.C. Candeal, E. Induráin and C. Rodríguez-Palmero, Continuous utility functions through scales, (2006), submitted.
2. G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, 1967.
3. G. Bosi, Continuous representations of interval orders based on induced preorders, Riv. Mat. Sci. economiche e sociali, XVIII, I (1995), 75-82.
4. G. Bosi and R. Isler, Representing preferences with nontransitive indifference by a single real-valued function, J. Math. Economics 24 (1995), 621-631.
5. G. Bosi, J.C. Candeal, E. Induráin, E. Oloriz and M. Zudaire, Numerical representations of interval orders, Order 18 (2001), 171-190.
6. G. Bosi, J.C. Candeal and E. Induráin, Natural topologies for interval-ordered structures and the continuous representation problem, (2005), preprint.
7. G. Bosi and G. B. Mehta, Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof, J. Math. Economics 38 (2002), 311-328.
8. G. Bosi and M. Zuanon, Continuous representability of homothetic preorders by means of sublinear order-preserving functions, Math. Soc. Sci. 45 (2003), 333-341.
9. D.S. Bridges, A numerical representation of preferences with intransitive indifference, J. Math. Economics 11 (1983), 25-42.
10. D.S. Bridges, Numerical representation of intransitive preferences on a countable set, J. Economic Theory 30 (1983), 213-217.
11. D.S. Bridges, Representing interval orders by a single real-valued function, J. Economic Theory 36 (1985), 149-155.
12. D.S. Bridges, Numerical representation of interval orders on a topological space, J. Economic Theory 38 (1986), 160-166.
13. D.S. Bridges and G.B. Mehta, Representations of Preference Orderings, Springer-Verlag, Berlin, 1995.
14. D.C.J. Burgess and M. Fitzpatrick, On separation axioms for certain types of ordered topological space, Math. Proc. Cam. Phil. Soc. 82 (1977), 59-65.
15. J.C. Candeal, E. Induráin and M. Zudaire, Continuous representability of interval orders, Applied General Topology 5 (2004), 213-230.
16. A. Chateauneuf, Continuous representation of a preference relation on a connected topological space, J. Math. Economics 16 (1987), 139-146.
17. G. Debreu, Continuity properties of Paretian utility, Int. Economic Review 5 (1964), 285-293.
18. P.C. Fishburn, Intransitive indifference with unequal indifference intervals, J. Math. Psychology 7 (1970), 144-149.
19. P.C. Fishburn, Interval Orders and Interval Graphs, Wiley, New York, 1985.
20. G. Herden, On the existence of utility functions, Math. Soc. Sciences 17 (1989), 297-313.
21. J.Y. Jaffray, Existence of a continuous utility function: an elementary proof, Econometrica 43 (1975), 981-983.
22. E. Oloriz, J.C. Candeal and E. Induráin, Representability of interval orders, J. Economic Theory 78 (1998), 219-227.