Preference Modelling

1. Front Matter

   Pages N2-VIII

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2. Binary Relations: Definitions, Representations, Basic Properties

   • Marc Roubens, Philippe Vincke

   Pages 1-5

3. The Concept of Preference Structure

   • Marc Roubens, Philippe Vincke

   Pages 6-10

4. Usual Preference Structures

   • Marc Roubens, Philippe Vincke

   Pages 11-53

5. Two New Preference Structures

   • Marc Roubens, Philippe Vincke

   Pages 54-64

6. Complete Valued Preference Structures

   • Marc Roubens, Philippe Vincke

   Pages 65-86

7. Complete Two-Valued Preference Structures

   • Marc Roubens, Philippe Vincke

   Pages 87-92

8. Back Matter

   Pages 93-96

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The following scheme summarizes the different families introduced in this chapter and the connections between them. Family of interval orders f Row-homogeneous Column-homogeneous Family of family of interval semi orders family of interval orders orders Homogeneous family of i nterva 1 orders Homogeneous family of semi orders Family of weak orders 85 5.13. EXAMPLES We let to the reader the verification of the following assertions. Example 1 is a family of interval orders which is neither row-homogeneous nor column-homogeneous. Example 2 is a column-homogeneous family of interval orders which is not row-homogeneous but where each interval order is a semiorder. Example 3 is an homogeneous family of interval orders which are not semiorders. Example 4 is an homogeneous family of semi orders . . 8 ~ __ --,b ~---i>---_ C a .2 d c Example Example 2 .8 .6 c .5 a 0 a d Example 3 Example 4 5.14. REFERENCES DOIGNON. J.-P •• Generalizations of interval orders. in E. Degreef and J. Van Buggenhaut (eds). T~ndS in MathematiaaZ PsyahoZogy. Elsevier Science Publishers B.V. (North-Holland), Amsterdam, 1984. FISHBURN. P.C., Intransitive indifference with unequal indifference intervals. J. Math. Psyaho.~ 7 (1970) 144-149. FISHBURN. P.C., Binary choice probabilities: on the varieties of stochastic transitivity. J. Math. Psyaho.~ 10 (1973) 327-352.

• Modelling
• modeling
• value-at-risk

• State University of Mons, Mons, Belgium

  Marc Roubens

• Free University of Brussels, Brussels, Belgium

  Philippe Vincke

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