Universal codomains to Represent Interval Orders

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.

[1]  P. Hammond,et al.  Handbook of Utility Theory , 2004 .

[2]  P. Swistak.  Some representation problems for semiorders , 1980 .

[3]  A. Chateauneuf.  Continuous representation of a preference relation on a connected topological space , 1987 .

[4]  H. J. Skala.  Nonstandard utilities and the foundation of game theory , 1974 .

[5]  D. Bouyssou,et al.  Utility Maximization, Choice and Preference , 2002 .

[6]  G. Cantor.  Beiträge zur Begründung der transfiniten Mengenlehre , 1897 .

[7]  Michael Pinedo,et al.  Planning and Scheduling in Manufacturing and Services , 2008 .

[8]  Peter C. Fishburn,et al.  Interval graphs and interval orders , 1985, Discret. Math..

[9]  P. Fishburn.  Intransitive indifference with unequal indifference intervals , 1970 .

[10]  R. Luce.  Semiorders and a Theory of Utility Discrimination , 1956 .

[11]  Juan Carlos Candeal,et al.  Interval-Valued Representability of Qualitative Data: the Continuous Case , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  Yakar Kannai,et al.  Non-standard concave utility functions , 1992 .

[13]  I. Gilboa,et al.  Numerical representations of imperfectly ordered preferences (a unified geometric exposition) , 1992 .

[14]  V. Novák.  Fuzzy sets and their applications , 1989 .

[15]  E. Induráin,et al.  Continuous representability of interval orders , 2004 .

[16]  W. E. Armstrong.  A NOTE ON TUE THEORY OF CONSUMER'S BEHAVIOUR , 1950 .

[17]  Juan Carlos Candeal,et al.  Numerical representability of semiorders , 2002, Math. Soc. Sci..

[18]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[19]  Juan Carlos Candeal,et al.  Lexicographic behaviour of chains , 1999 .

[20]  E. Induráin,et al.  Representability of Interval Orders , 1998 .

[21]  G. Mehta.  Preference and utility , 1998 .

[22]  Gerhard Herden,et al.  The Debreu Gap Lemma and some generalizations , 2004 .

[23]  K M Eriksson.  Book Review: Planning and Scheduling in Manufacturing and Services. Michael L. Pinedo, Springer-Verlag, £46.00 (ISBN 0 387 22198 0): , 2005 .

[24]  T. William,et al.  Surveys in Combinatorics, 1997: New Perspectives on Interval Orders and Interval Graphs , 1997 .

[25]  A. Tversky.  Intransitivity of preferences. , 1969 .

[26]  Juan Carlos Candeal,et al.  Representability of binary relations through fuzzy numbers , 2006, Fuzzy Sets Syst..

[27]  D. Bridges,et al.  Representations of Preferences Orderings , 1995 .

[28]  J. Chipman.  The Foundations of Utility , 1960 .

[29]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[30]  Juan Carlos Candeal,et al.  Numerical Representations of Interval Orders , 2001, Order.

[31]  Kenneth L. Manders.  On jnd representations of semiorders , 1981 .

[32]  D. Bridges.  Numerical representation of intransitive preferences on a countable set , 1983 .

[33]  Peter C. Fishburn,et al.  LEXICOGRAPHIC ORDERS, UTILITIES AND DECISION RULES: A SURVEY , 1974 .

[34]  Patrick Suppes,et al.  Foundational aspects of theories of measurement , 1958, Journal of Symbolic Logic.

[35]  Peter C. Fishburn,et al.  Intransitive Indifference in Preference Theory: A Survey , 1970, Oper. Res..

[36]  P. Fishburn.  Interval representations for interval orders and semiorders , 1973 .

[37]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[38]  Jean-Paul Doignon,et al.  On realizable biorders and the biorder dimension of a relation , 1984 .

[39]  G. Bosi,et al.  Representing preferences with nontransitive indifference by a single real-valued function☆ , 1995 .

[40]  Didier Dubois,et al.  Fuzzy sets and their applications: Vilem Novak, translated from Czechoslovakian. Bristol and Philadelphia: Adam Hilger, 1989, 248 pages. , 1991 .