Some Basic Techniques for Constructing Value Functions

  • Po-Lung Yu
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 30)


Once we are convinced that the existence conditions for the value function are satisfied, or are willing to take the risk to simplify the problem so that we can focus on a value function, we may begin to construct a value function to represent the revealed preference information. One must realize that such an attempt is tantamount to the acceptance of the assumptions described in the previous sections. If one is not sure that the assumptions hold, then at best one can regard the value function to be derived as an approximation of the preference. Thus, admittedly, errors and biases may exist in the preference representation.


Decision Maker Linear Programming Problem Consistency Condition Tangent Plane Ideal Point 
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Suggested Reading

  1. 2.
    Addelman, S., Orthogonal main-effect plans for asymmetrical factorial experiments, Technometrics4, 21–46 (1962).MathSciNetMATHCrossRefGoogle Scholar
  2. 7.
    Apostol, T. M., Calculus, Vol. II: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability, Blaisdell, Waltham, Massachusetts (1969).Google Scholar
  3. 22.
    Barron, F. H., and Person, H. B., Assessment of multiplicative utility functions via holistic judgments, Organ. Behay. Human Performance24, 147–166 (1979).CrossRefGoogle Scholar
  4. 87.
    Chu, A. T. W., Kalaba, R. E., and Spingarn, K., A comparison of two methods for determining the weights of belonging to fuzzy sets, J. Opt. Theory Appl.27, 531–538 (1979).MathSciNetMATHCrossRefGoogle Scholar
  5. 91.
    Cogger, K. O., and Yu, P. L., Eigen weight vectors and least distance approximation for revealed preference in pairwise weight ratios, J. Optim. Theory Appl.46, (4) (1985).Google Scholar
  6. 222.
    Hwang, C. L., and Yoon, K., Multiple Attribute Decision Making-Methods and Applications: A State-of-the-Art Survey, Springer-Verlag, New York (1981).CrossRefGoogle Scholar
  7. 223.
    Hwang, C. L., and Masud, A. S. M., (in collaboration with S. R. Paidy and K. Yoon), Multiple Objective Decision Making-Methods and Applications: A State-of-the-Art Survey, Springer-Verlag, New York (1979).MATHCrossRefGoogle Scholar
  8. 228.
    Isaacs, R., Differential Games, Wiley, New York (1965).MATHGoogle Scholar
  9. 250.
    Keeney, R. L., A decision analysis with multiple objectives: The Mexico City Airport, Bell J. Econ. Manage.4, 101–117 (1973).CrossRefGoogle Scholar
  10. 254.
    Keeney, R. L., and Raiffa, H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley, New York (1976).Google Scholar
  11. 287.
    Leitmann, G., An Introduction to Optimal Control, McGraw-Hill, New York (1966).MATHGoogle Scholar
  12. 365.
    Rao, C. R., Linear Statistical Inference and Its Applications, Wiley, New York, (1973).MATHCrossRefGoogle Scholar
  13. 389.
    Saaty, T. L., A scaling method for priorities in hierarchical structures, J. Math. Psycho!. 15, 234–281 (1977).MathSciNetMATHCrossRefGoogle Scholar
  14. 391.
    Saaty, T. L., The Analytic Hierarchy Process, McGraw-Hill, New York, (1980).MATHGoogle Scholar
  15. 421.
    Srinivasan, V., and Shocker, A. D., Estimating the weights for multiple attributes in a composite criterion using pairwise judgements, Psychometrika38, 473–493 (1973).MathSciNetMATHCrossRefGoogle Scholar
  16. 422.
    Srinivasan, V., and Shocker, A. D., Linear programming techniques for multidimensional analysis of preference, Psychometrika38, 337–369 (1973).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Po-Lung Yu
    • 1
  1. 1.University of KansasLawrenceUSA

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