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UNIVERSAL CODOMAINS TO REPRESENT INTERVAL ORDERS

Depto. de Análisis Económico, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza. c/ Doctor Cerrada 1-3, 50005 Zaragoza, Spain

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JAVIER GUTIÉRREZ GARCÍA

Depto. de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain

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, and

ESTEBAN INDURÁIN

Depto. de Matemáticas, Universidad Pública de Navarra, Campus Arrosadía, 31006 Pamplona, Spain

Corresponding author.

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https://doi.org/10.1142/S0218488509005814Cited by:11 (Source: Crossref)

Abstract

Given a binary relation defined on a set, we study its representability by means of a monotonic function that takes values on a suitable universal codomain (that depends on the kind of relation considered). We pay an special attention to the representability of interval orders, studying their alternative universal codomains, some of them equivalent to the set of symmetric triangular fuzzy numbers.

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References

G. Cantor, Math. Ann. 46, 481 (1895), DOI: 10.1007/BF02124929. Crossref, Google Scholar
G. Cantor, Math. Ann. 49, 207 (1897), DOI: 10.1007/BF01444205. Crossref, Google Scholar
G. Birkhoff , Lattice Theory , 3rd edn. ( American Mathematical Society , Providence, RI , 1967 ) . Google Scholar
D. S. Bridges and G. B. Mehta , Representations of Preference Orderings ( Springer , Berlin , 1995 ) . Crossref, Google Scholar
G. B. Mehta, Handbook of Utility Theory, eds. S. Barberà, P. Hammond and C. Seidl (Kluwer Acad. Pub., Dordrecht, 1998) pp. 1–47. Google Scholar
F. Aleskerov , D. Bouyssou and B. Monjardet , Utility Maximization, Choice and Preference , 2nd edn. ( Springer , Berlin , 2007 ) . Google Scholar
D. S. Bridges, J. Econom. Theory 30, 213 (1983), DOI: 10.1016/0022-0531(83)90103-5. Crossref, Web of Science, Google Scholar
G. Bosi and R. Isler, J. Math. Econom. 24, 621 (1995), DOI: 10.1016/0304-4068(94)00706-G. Crossref, Web of Science, Google Scholar
P. C. Fishburn, J. Math. Psych. 7, 144 (1970), DOI: 10.1016/0022-2496(70)90062-3. Crossref, Web of Science, Google Scholar
P. C. Fishburn, Oper. Res. 18(2), 207 (1970), DOI: 10.1287/opre.18.2.207. Crossref, Web of Science, Google Scholar
P. C. Fishburn, J. Math. Psych. 10, 91 (1973), DOI: 10.1016/0022-2496(73)90007-2. Crossref, Web of Science, Google Scholar
P. C. Fishburn , Interval Orders and Interval Graphs ( Wiley , New York , 1985 ) . Crossref, Google Scholar
A. Tversky, Psychological Rev. 76(1), 31 (1969), DOI: 10.1037/h0026750. Crossref, Web of Science, Google Scholar
N. Wiener, Proc. Cambridge Philos. Soc. 17, 441 (1914). Web of Science, Google Scholar
P. Swistak, J. Math. Psych. 21(2), 124 (1980). Crossref, Web of Science, Google Scholar
W. E. Armstrong, Oxford Econom. Papers 2, 119 (1950). Crossref, Web of Science, Google Scholar
G. Herden and G. B. Mehta, J. Math. Econom. 40(7), 747 (2004), DOI: 10.1016/j.jmateco.2003.06.002. Crossref, Web of Science, Google Scholar
J. S. Chipman, Econometrica 28(2), 193 (1960), DOI: 10.2307/1907717. Crossref, Web of Science, Google Scholar
I. Fleischer, Fund. Math. 49, 147 (1961). Crossref, Google Scholar
M. K. Richter , Rational Choice, in Preferences, Utility and Demand , eds. Chipman et al. ( Harcourt Brace Jovanovich , New York , 1971 ) . Google Scholar
H. J. Skala, Int. J. Game Theory 3, 67 (1974), DOI: 10.1007/BF01766393. Crossref, Google Scholar
P. C. Fishburn, Management Sci. 20(11), 1442 (1974), DOI: 10.1287/mnsc.20.11.1442. Crossref, Web of Science, Google Scholar
Y. Kannai, J. Math. Econom. 21, 51 (1992), DOI: 10.1016/0304-4068(92)90021-X. Crossref, Web of Science, Google Scholar
D. Scott and P. Suppes, J. Symbolic Logic 23, 113 (1958). Crossref, Google Scholar
J. C. Candeal and E. Induráin, Arch. Math. 72, 145 (1999), DOI: 10.1007/s000130050315. Crossref, Web of Science, Google Scholar
M. J. Campión, J. C. Candeal and E. Induráin, Fuzzy Sets and Systems 157, 1 (2006). Crossref, Web of Science, Google Scholar
R. D. Luce, Econometrica 24, 178 (1956), DOI: 10.2307/1905751. Crossref, Web of Science, Google Scholar
J. C. Candeal, E. Induráin and M. Zudaire, Math. Social Sci. 43(1), 61 (2002), DOI: 10.1016/S0165-4896(01)00082-8. Crossref, Web of Science, Google Scholar
G. Bosiet al., Int. J. Uncertainty, Fuzziness and Knowledge-based Systems 15(3), 299 (2007), DOI: 10.1142/S0218488507004698. Link, Web of Science, Google Scholar
B. A. Davey and H. A. Priestley , Introduction to Lattices and Order ( Cambridge University Press , Cambridge , 1990 ) . Google Scholar
W. T. Trotter, Surveys in Combinatorics, London Math. Soc. Lecture Note Ser. 241 (Cambridge University Press, Cambridge, 1997) pp. 237–286. Google Scholar
M. Pinedo , Planning and Scheduling in Manufacturing and Services ( Springer-Verlag , New York , 2005 ) . Google Scholar
G. Bosiet al., Order 18, 171 (2001), DOI: 10.1023/A:1011974420295. Crossref, Google Scholar
E. Olóriz, J. C. Candeal and E. Induráin, J. Econom. Theory 78(1), 219 (1998). Crossref, Web of Science, Google Scholar
J. P. Doignon, A. Ducamp and J. C. Falmagne, J. Math. Psych. 28, 73 (1984), DOI: 10.1016/0022-2496(84)90020-8. Crossref, Web of Science, Google Scholar
A. Kaufmann and M. M. Gupta , Introduction to Fuzzy Arithmetic, Theory and Applications ( Van Nostrand Reinhold Company , New York , 1985 ) . Google Scholar
D. Dubois and H. Prade, Int. J. Systems Sci. 9(6), 613 (1978), DOI: 10.1080/00207727808941724. Crossref, Web of Science, Google Scholar
V. Novák , Fuzzy Sets and Their Applications ( Adam Hilger , Bristol and Philadelphia , 1989 ) . Google Scholar
K. L. Manders, J. Math. Psych. 24, 224 (1981), DOI: 10.1016/0022-2496(81)90044-4. Crossref, Web of Science, Google Scholar
A. Beja and I. Gilboa, J. Math. Psych. 36, 426 (1992), DOI: 10.1016/0022-2496(92)90030-B. Crossref, Web of Science, Google Scholar
J. Aczél , A Short Course on Functional Equations ( D. Reidel , Dordrecht , 1987 ) . Crossref, Google Scholar
J. C. Candeal, E. Induráin and M. Zudaire, Appl. Gen. Topol. 5(2), 213 (2004). Crossref, Web of Science, Google Scholar
A. Chateauneuf, J. Math. Econom. 16, 139 (1987), DOI: 10.1016/0304-4068(87)90003-6. Crossref, Web of Science, Google Scholar