The Expected Value of Imperfect Information to Fuzzy Programming

  • Mingfa Zheng
  • Guoli Wang
  • Guangxing Kou
  • Jia Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5552)


The paper is concerned with finding the expected value of imperfect information to two-stage fuzzy programming. In this paper we firstly present the definition which is the sum of pairs expected value, then obtain the definition of expected value of imperfect information based on the concept, and discuss its rationality. In addition, several numerical examples are also given to explain the definitions. The results obtained in this paper can be used to fuzzy optimization as we design algorithm to estimate the value of imperfect information.


Fuzzy programming Expected value of perfect information Expected value of imperfect information 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zadeh, L.A.: Fuzzy sets as a basic for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)CrossRefzbMATHGoogle Scholar
  2. 2.
    de Cooman, G., Kerre, E.E., Vanmassenhove, F.: Possibility theory: an Integral Theoretic Approach. Fuzzy Sets Syst. 46, 287–299 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Liu, B.D.: Toward fuzzy optimization without mathematical ambiguity. Fuzzy Optimization and Decision Making 1, 43–63 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Liu, B.D., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10, 445–450 (2002)CrossRefGoogle Scholar
  5. 5.
    Liu, B.D.: Uncertainty theory: An introduction to it’s axiomatic foundations. Springer, Germany (2004)CrossRefGoogle Scholar
  6. 6.
    Liu, B.D.: Theory and practice of uncertainty programming. Physica-Verlag, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Kall, P.: Stochastic Linear programming. Springer, Germany (1976)Google Scholar
  8. 8.
    Birge, J.R., Louveaux, F.: Introduction to stochastic programming.Springer, New York (1997)Google Scholar
  9. 9.
    Kall, P., Wallace, S.W.: Stochastic Programming. Chichester, Wiley (1994)Google Scholar
  10. 10.
    Liu, Y.K.: Fuzzy Programming with Recouse. International Journal of Uncertainty, fuzzyiness and Knowledge-based Systems 13, 382–413 (2005)Google Scholar
  11. 11.
    Wang, S.H., Liu, Y.K.: Fuzzy Two-Stage Mathematical Programming Problems. In: 2th IEEE International Conference on Machine Learning and Cebernetics, pp. 2638–2643. IEEE Press, New York (2003)Google Scholar
  12. 12.
    Nahmias, S.: Fuzzy variables. Fuzzy Sets Syst. 1, 97–101 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Liu, Y.K., Gao, J.: The independence of fuzzy variable with applications to fuzzy random optimation. International Journal of Uncertainty, Fuzziness Knowledge-Based Systems 15, 1–20 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, Y.K., Wang, S.: Theory of Fuzzy Random Optimization. China Agricultural University Press, Beijing (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mingfa Zheng
    • 1
  • Guoli Wang
    • 2
  • Guangxing Kou
    • 1
  • Jia Liu
    • 1
  1. 1.Department of Applied Mathematics and PhysicsAir Force Engineering University, Xi’anChina
  2. 2.College of Mathematics & Computer ScienceHebei University, BaodingChina

Personalised recommendations