The Absolute Additivity and Fuzzy Additivity of Sugeno Integral

  • Congxin Wu
  • Liang Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3930)


In this paper, based on the foundation of the discussion of the Sugeno integral for real functions which was presented by Wu Congxin and Mamadou in 2003, we introduce and consider the concept of the absolute additivity of the Sugeno integral for real functions. We also discuss the fuzzy additivity of the Sugeno integral for real functions. For these two kinds of additivity, we obtain two necessary and sufficient conditions, a sufficient condition, a necessary condition and several counter examples.


Genetic Algorithm Real Function Nonnegative Function Fuzzy Measure Solute Additivity 
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.
    Sugeno, M.: Theory of fuzzy integral and its application. Ph. D. Thesis. Tokyo Institute of Technology (1974)Google Scholar
  2. 2.
    Ralescu, D., Adams, G.: The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum Press, New York (1992)MATHGoogle Scholar
  4. 4.
    Pap, E.: Null-Additive Set Functions. Kluwer, Dordecht (1995)MATHGoogle Scholar
  5. 5.
    Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integral: Theory and Applications. Physica-Verlag, Heideberg (2000)MATHGoogle Scholar
  6. 6.
    Wu, C., Mamadou, T.: An extension on Sugeno integral. Fuzzy Sets and Systems 138, 537–550 (2003)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Sipos, J.: Integral with respect to a pre-measure. Math. Slovaca 29, 141–155 (1979)MATHMathSciNetGoogle Scholar
  8. 8.
    Marinova, I.: Integration with respect to a ⊕measure. Math. Slovaca 36, 15–24 (1986)MATHMathSciNetGoogle Scholar
  9. 9.
    Kolesarova, A.: Integration of real functions with respect to a ⊕ measure. Math. Slovaca 46, 41–52 (1996)MATHMathSciNetGoogle Scholar
  10. 10.
    Narukawa, Y., Murofushi, T., Sugeno, M.: Extension and representation of comonotonically additive functionals. Fuzzy Sets and Systems 121, 217–226 (2000)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Klement, E.P., Ralescu, D.A.: Nonlinearity of the fuzzy integral. Fuzzy sets and systems 11, 309–315 (1983)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Wang, Z., Leung, K., Wang, J.: Determining nonnegative monotone set function based on Sugeno’s integral: an application of genetic algorithms. Fuzzy Sets and Systems 112, 155–164 (2000)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Congxin Wu
    • 1
  • Liang Zhao
    • 1
  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina

Personalised recommendations