Preference Modelling
Published on 1. September 1985
Book
Paperback/Softback
VIII, 98 pages
978-3-540-15685-7 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1985
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 98 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 7 mm
Weight
202 gr
ISBN-13
978-3-540-15685-7 (9783540156857)
DOI
10.1007/978-3-642-46550-5
Schweitzer Classification
Persons
Professor Dr. Günter Bentele ist Inhaber des Lehrstuhls für Öffentlichkeitsarbeit/Public Relations am Institut für Kommunikations- und Medienwissenschaft der Universität Leipzig.
Content
1: Binary Relations: Definitions, Representations, Basic Properties.- 1.1. Binary relations.- 1.2. Graph representation of binary relations.- 1.3. Coding the binary relations.- 1.4. Matrix representation of binary relations.- 1.5. Basic properties of binary relations.- 1.6. Particular binary relations.- 1.7. Graph interpretation of the properties.- 1.8. Algebraic interpretation of the properties.- 1.9. References.- 2: The Concept of Preference Structure.- 2.1. Preference, indifference, incomparability.- 2.2. Preference structure.- 2.3. Important agreement.- 2.4. Characteristic relation of a preference structure.- 2.5. Graph representation of a preference structure.- 2.6. Coding the preference structure.- 2.7. Example.- 2.8. References.- 3: Usual Preference Structures.- 3.1. Tournament structure.- 3.2. Total order structure.- 3.3. Weak order structure.- 3.4. Total interval order structure.- 3.5. Total semiorder structure.- 3.6. Partial order structure.- 3.7. Quasi order structure.- 3.8. References.- 4: Two New Preference Structures.- 4.1. Partial interval order structure.- 4.2. Partial semiorder structure.- 4.3. References.- 5: Complete Valued Preference Structures.- 5.1. Definition.- 5.2. Important remark.- 5.3. Particular case.- 5.4. Graph representation.- 5.5. Matridal representation.- 5.6. Particular complete valued preference structures.- 5.7. Binary relations and various properties related to a complete valued preference structure.- 5.8. Characterizations of the families defined in section 5.6...- 5.9. Functional representation of a valued preference structure.- 5.10. Roberts homogeneous families of semiorders.- 5.11. Families of weak orders.- 5.12. Summary.- 5.13. Examples.- 5.14. References.- 6: Complete Two-Valued Preference Structures.- 6.1. Introduction.- 6.2.Two-valued preference structures with constant thresholds.- 6.3. Example.- 6.4. References.