Convex Interval and Fuzzy (Valued) Functions with Functionals

  • Bing-yuan Cao
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 54)


The writer in this paper, on the foundation of interval and fuzzy (value) function, interval and fuzzy (value) functional variation, puts forward a concept on convex interval and convex fuzzy (value) function with functional, gives the definition of a convex function and convex functional about an interval, a common function at fuzzy points, a fuzzy-valued function at common points and a fuzzy-valued function at fuzzy points, and judges their convexity condition. This lays a foundation on the application of fuzzy optimal theories and fuzzy variation methods at physical and approximate calculation.


Convex interval function with functional Convex Fuzzy (valued) function with functional Fuzzy point Fuzzy optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cao, B.Y.: Variation of Interval-valued and Fuzzy Functional. In: 4th IFSA Congress, Brussels, pp. 21–24 (1991)Google Scholar
  2. 2.
    Cao, B.Y.: Variation of condition extremum in interval and fuzzy valued functional. J. Fuzzy Mathematics 9(4), 845–852 (2001)zbMATHGoogle Scholar
  3. 3.
    Cao, B.Y.: Variation of condition extremum with fuzzy variable. J. Fuzzy Mathematics 7(3), 559–564 (1999)zbMATHGoogle Scholar
  4. 4.
    Jiaten, M.F.: Variational method and its application. Science technique publisher of Shanghai, Shanghai (1961)Google Scholar
  5. 5.
    Cen, Y.T.: Newton-Leibniz formulas of interval-valued function and fuzzy-valued function. J. Fuzzy Mathematics 3-4, 13–18 (1987)MathSciNetGoogle Scholar
  6. 6.
    Wang, D.M., Lou, C.Z.: Extension of fuzzy differenial calculus. Fuzzy Mathematics 1, 75–80 (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bing-yuan Cao
    • 1
  1. 1.Guangzhou Higher Education Mega CenterGuangzhou UniversityChina

Personalised recommendations