Universal codomains to represent interval orders

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 17, Issue 2, 2009, Pages 197-219

  Candeal, Juan Carlos ^a   Gutiérrez García, Javier ^b   Induráin, Esteban ^c  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^c PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Continuous representations of orderings; Fuzzy numbers; Interval orders; Universal codomains

Indexed keywords

BINARY RELATION; CONTINUOUS REPRESENTATION OF ORDERING; FUZZY NUMBERS; INTERVAL ORDERS; MONOTONIC FUNCTIONS; REPRESENTABILITY; SYMMETRICS; TRIANGULAR FUZZY NUMBERS; UNIVERSAL CODOMAIN;

FUZZY RULES;

EID: 65249178318     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488509005814     Document Type: Article

References (43)

1. G. Cantor, Beiträge zur Begriindung der transfiniten Mengenlehre I, Math. Ann. 46 (1895) 481-512.
2. G. Cantor, Beiträge zur Begriindung der transfiniten Mengenlehre II, Math. Ann. 49 (1897) 207-246.
3. G. Birkhoff, Lattice Theory, 3rd edn. (American Mathematical Society, Providence, RI, 1967).
4. D. S. Bridges and G. B. Mehta, Representations of Preference Orderings (Springer, Berlin, 1995).
5. G. B. Mehta, Preference and utility, in Handbook of Utility Theory, eds. S. Barberà and P. Hammond, C. Seidl (Kluwer Acad. Pub., Dordrecht, 1998), pp. 1-47.
6. F. Aleskerov, D. Bouyssou and B. Monjardet, Utility Maximization, Choice and Preference, 2nd edn. (Springer, Berlin, 2007).
7. D. S. Bridges, Numerical representations of intransitive preferences on a countable set, J. Econom. Theory 30 (1983) 213-217.
8. G. Bosi and R. Isler, Representing preferences with nontransitive indifference by a single real-valued function, J. Math. Econom. 24 (1995) 621-631.
9. P. C. Fishburn, Intransitive indifference with unequal indifference intervals, J. Math. Psych. 7 (1970) 144-149.
10. P. C. Fishburn, Intransitive indifference in preference theory: a survey, Oper. Res. 18(2) (1970) 207-228.
11. P. C. Fishburn, Interval representations for interval orders and semiorders, J. Math. Psych. 10 (1973) 91-105.
12. P. C. Fishburn, Interval Orders and Interval Graphs (Wiley, New York, 1985).
13. A. Tversky, Intransitivity of preferences, Psychological Rev. 76(1) (1969) 31-48.
14. N.Wiener, Contribution to the theory of relative position, Proc. Cambridge Philos. Soc. 17 (1914) 441-449.
15. P. Swistak, Some representation problems for semiorders, J. Math. Psych. 21(2) (1980) 124-135.
16. W. E. Armstrong, A note on the theory of consumer's behavior, Oxford, Econom. Papers 2 (1950) 119-122.
17. G. Herden and G. B. Mehta, The Debreu Gap Lemma and some generalizations, J. Math. Econom. 40(7) (2004) 747-769.
18. J. S. Chipman, The foundations of utility, Econometrtca 28(2) (1960) 193-224.
19. I. Fleischer, Embedding linearly ordered sets in real lexicographic products, Fund. Math. 49 (1961) 147-150.
20. M. K. Richter, Rational Choice, in Preferences, Utility and Demand, eds. Chipman et al. (Harcourt Brace Jovanovich, New York, 1971).
21. H. J. Skala, Nonstandard utilities and the foundations of game theory, Int. J. Game Theory 3 (1974) 67-81.
22. P. C. Fishburn, Lexicographic orders, utilities and decision rules: a survey. Management Set. 20 (11) (1974) 1442-1471.
23. Y. Kannai, Non-standard concave utility functions, J. Math. Econom. 21 (1992) 51-58.
24. D. Scott and P. Suppes, Foundational aspects of theories of measurement, J. Symbolic Logtc 23 (1958) 113-128.
25. J. C. Candeal and E. Induráin, Lexicographic behaviour of chains, Arch. Math. 72 (1999) 145-152.
26. M. J. Campion, J. C. Candeal and E. Induráin, Representabilíty of binary relations through fuzzy numbers, Fuzzy Sets and Systems 157 (2006) 1-19.
27. R. D. Luce, Semiorders and a theory of utility discrimination, Econometrica 24 (1956) 178-191.
28. J. C. Candeal, E. Induráin and M. Zudaire, Numerical representability of semiorders, Math. Social Set. 43(1) (2002) 61-77.
29. G. Bosi, M. J. Campion, J. C. Candeal and E. Induráin, Interval-valued representability of qualitative data: the continuous case, Int. J. Uncertainty, Fuzziness and Knowledge-based Systems 15(3) (2007) 299-319.
30. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order (Cambridge University Press, Cambridge, 1990).
31. W. T. Trotter, New perspectives on interval orders and interval graphs, in Surveys in Combinatorics, London Math. Soc. Lecture Note Ser. 241, (Cambridge University Press, Cambridge, 1997), pp. 237-286.
32. M. Pinedo, Planning and Scheduling in Manufacturing and Services (Springer-Verlag, New York, 2005).
33. G. Bosi, J. C. Candeal, E. Induráin, E. Olóriz and M. Zudaire, Numerical representations of interval orders, Order 18 (2001) 171-190.
34. E. Olóriz, J. C. Candeal and E. Induráin, Representability of interval orders, J. Econom. Theory 78(1) (1998) 219-227.
35. J. P. Doignon, A. Ducamp and J. C. Falmagne, On realizable biorders and the biorder dimension of a relation, J. Math. Psych. 28 (1984) 73-109.
36. A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic, Theory and Applications (Van Nostrand Reinhold Company, New York, 1985).
37. D. Duboìs and H. Prade, Operations on fuzzy numbers, Int. J. Systems Sci. 9(6) (1978) 613-626.
38. V. Novak, Fuzzy Sets and Their Applications (Adam Hilger, Bristol and Philadelphia, 1989).
39. K. L. Manders, On JND representations of semiorders, J. Math. Psych. 24 (1981) 224-248.
40. A. Beja and I. Gilboa, Numerical representations of imperfectly ordered preferences. (A unified geometrical exposition), J. Math. Psych. 36 (1992) 426-449.
41. J. Aczél, A Short Course on Functional Equations (D. Reidel, Dordrecht, 1987).
42. J. C. Candeal, E. Induráin and M. Zudaire, Continuous representability of interval orders, Appl. Gen. Topol. 5(2) (2004) 213-230.
43. A. Chateauneuf, Continuous representation of a preference relation on a connected topological space, J. Math. Econorn. 16 (1987) 139-146.