Average level of a fuzzy set

  • Dan A. Ralescu
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 87)


In this paper the average level set of a fuzzy set is defined on the basis of the Kudo-Aumann integral of a set-valued mapping. Some properties of the average level as well as its particularization for some special cases are analyzed.


Fuzzy Number Triangular Fuzzy Number Belief Function Fuzzy Random Variable Convex Level 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aumann, R.J. (1965). Integrals of set-valued functions, J. Math. Anal. Appl. 12, 1–12.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Debreu, A. (1967). Integration of correspondences, Proc. Fifth Berkeley Symp. Math. Stat. Prob., 351–372.Google Scholar
  3. 3.
    Dubois, D. and Prade, H. (1987). The mean value of a fuzzy number, Fuzzy Sets and Systems 24, 279–300.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Heilpern, S. (1992). The expected value of a fuzzy number, Fuzzy Sets and Systems 47, 81–86.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Klement, E.P., Puri, M.L. and Ralescu, D.A (1986). Limit theorems for fuzzy random variables, Proc. R. Soc. Lond. A407, 171–182.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Negoita, C.V. and Ralescu, D.A. (1974), Fuzzy Sets and Their Applications, Wiley, New York.MATHGoogle Scholar
  7. 7.
    Wasserman, L.A. (1990), Prior envelopes based on belief functions, Annals of Statistics 18, 454–464.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dan A. Ralescu
    • 1
  1. 1.Department of Matematical SciencesUniversity of CincinnatiCincinnatiUSA

Personalised recommendations