Isotonies on ordered cones through the concept of a decreasing scale

Mathematical social sciences

Volumn 54, Issue 2, 2007, Pages 115-127

  Bosi, Gianni ^a   Campión, María J ^b   Candeal, Juan C ^c   Induráin, Esteban ^b   Zuanon, Magalì E ^d  

^a UNIVERSITY OF TRIESTE   (Italy)

^b PUBLIC UNIVERSITY OF NAVARRE   (Spain)

^c UNIVERSITY OF ZARAGOZA   (Spain)

^d UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Decreasing scales; Isotonies; Numerical representability of ordered structures; Ordered cones; Real valued functions

Indexed keywords

EID: 34547851179     PISSN: 01654896     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mathsocsci.2007.05.001     Document Type: Article

References (28)

1. Bosi G., and Zuanon M.E. Continuous representability of homothetic preorders by means of sublinear order-preserving functions. Mathematical Social Sciences 45 3 (2003) 333-341
2. Bosi G., Candeal J.C., and Induráin E. Continuous representability of homothetic preferences by means of homogeneous utility functions. Journal of Mathematical Economics 33 (2000) 291-298
3. Bosi G., Campión M.J., Candeal J.C., Induráin E., and Zuanon M.E. Numerical isotonies of preordered semigroups through the concept of a scale. Mathematica Pannonica 16 1 (2005) 65-77
4. Bridges D.S., and Mehta G.B. Representations of Preference Orderings (1995), Ed. Springer-Verlag, Berlin
5. Burgess D.C.J., and Fitzpatrick M. On separation axioms for certain types of ordered topological space. Mathematical Proceedings of the Cambridge Philosophical Society 82 (1977) 59-65
6. Candeal J.C., De Miguel J.R., and Induráin E. Topological additively representable semigroups. Journal of Mathematical Analysis and Applications 210 (1997) 375-389
7. Candeal J.C., and Induráin E. Homothetic and weakly homothetic preferences. Journal of Mathematical Economics 24 (1995) 147-158
8. Candeal J.C., Induráin E., and Mehta G.B. Order preserving functions on ordered topological vector spaces. Bulletin of the Australian Mathematical Society 60 (1999) 55-65
9. Candeal J.C., De Miguel J.R., and Induráin E. Expected utility from additive utility on semigroups. Theory and Decision 53 (2002) 87-94
10. Clark S.A. The measurement of qualitative probability. Journal of Mathematical Psychology 44 (2000) 464-479
11. De Miguel J.R., Candeal J.C., and Induráin E. Archimedeaness and additive utility on totally ordered semigroups. Semigroup Forum 52 (1996) 335-347
12. Dow J., and Werlang S.R.d.C. Homothetic preferences. Journal of Mathematical Economics 21 (1992) 389-394
13. Dugundji J. Topology (1966), Allyn and Bacon, Boston
14. Fishburn P.C. The Foundations of Expected Utility (1982), D. Reidel., Dordrecht, The Netherlands
15. Fuchs L. Partially Ordered Algebraic Systems (1963), Pergamon Press, Oxford, U.K
16. Gillman L., and Jerison M. Rings of Continuous Functions (1960), Springer Verlag, New York
17. Herden G. On the existence of utility functions. Mathematical Social Sciences 17 (1989) 297-313
18. Herden G. On the existence of utility functions II. Mathematical Social Sciences 18 (1989) 107-117
19. Herden G. On some equivalent approaches to mathematical utility theory. Mathematical Social Sciences 29 (1995) 19-31
20. Herden G., and Pallack A. On the continuous analogue of the Szpilrajn Theorem I. Mathematical Social Sciences 43 (2002) 115-134
21. Hofmann K.H., and Lawson J.D. Linearly ordered semigroups: historical origins and A.H. Clifford's influence. In: Hofmann H., and Mislove W. (Eds). Semigroup theory and its applications (1996), Cambridge University Press, Cambridge, U.K 15-39
22. Katzner D.W. Static Demand Theory (1970), Macmillan, London
23. Keimel, K., and Roth, W., 1992. Ordered Cones and Approximation. Lecture Notes in Mathematics 1517. Ed. Springer-Verlag. Berlin.
24. Kelley J.L. General Topology (1955), Van Nostrand, New York
25. Nachbin L. Topology and Order (1965), Van Nostrand Reinhold, New York
26. Rudin W. Functional Analysis (1991), Mc Graw-Hill, New York
27. Uryshon P. Über die Mächtigkeit der zusammenhangenden Mengen. Mathematische Annalen 94 (1925) 262-295
28. Yosida K., and Hewitt E.M. Finitely additive measures. Transactions of the American Mathematical Society 72 (1952) 46-66