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The Absolute Additivity and Fuzzy Additivity of Sugeno Integral

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Advances in Machine Learning and Cybernetics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3930))

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Abstract

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.

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References

  1. Sugeno, M.: Theory of fuzzy integral and its application. Ph. D. Thesis. Tokyo Institute of Technology (1974)

    Google Scholar 

  2. Ralescu, D., Adams, G.: The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum Press, New York (1992)

    MATH  Google Scholar 

  4. Pap, E.: Null-Additive Set Functions. Kluwer, Dordecht (1995)

    MATH  Google Scholar 

  5. Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integral: Theory and Applications. Physica-Verlag, Heideberg (2000)

    MATH  Google Scholar 

  6. Wu, C., Mamadou, T.: An extension on Sugeno integral. Fuzzy Sets and Systems 138, 537–550 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Sipos, J.: Integral with respect to a pre-measure. Math. Slovaca 29, 141–155 (1979)

    MATH  MathSciNet  Google Scholar 

  8. Marinova, I.: Integration with respect to a ⊕measure. Math. Slovaca 36, 15–24 (1986)

    MATH  MathSciNet  Google Scholar 

  9. Kolesarova, A.: Integration of real functions with respect to a ⊕ measure. Math. Slovaca 46, 41–52 (1996)

    MATH  MathSciNet  Google Scholar 

  10. Narukawa, Y., Murofushi, T., Sugeno, M.: Extension and representation of comonotonically additive functionals. Fuzzy Sets and Systems 121, 217–226 (2000)

    Article  MathSciNet  Google Scholar 

  11. Klement, E.P., Ralescu, D.A.: Nonlinearity of the fuzzy integral. Fuzzy sets and systems 11, 309–315 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Congxin Wu & Liang Zhao

Authors
  1. Congxin Wu
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  2. Liang Zhao
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Editor information

Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, P.O. Box, Hong Kong, China

    Daniel S. Yeung

  2. School of Creative Media, City University of Hong Kong,, China

    Zhi-Qiang Liu

  3. Department of Mathematics and Computer Science, Hebei University, 071002, Baoding, Hebei, P.R. China

    Xi-Zhao Wang

  4. School of Electrical and Information Engineering, University of Sydney, 2006, NSW, Australia

    Hong Yan

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© 2006 Springer-Verlag Berlin Heidelberg

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Wu, C., Zhao, L. (2006). The Absolute Additivity and Fuzzy Additivity of Sugeno Integral. In: Yeung, D.S., Liu, ZQ., Wang, XZ., Yan, H. (eds) Advances in Machine Learning and Cybernetics. Lecture Notes in Computer Science(), vol 3930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11739685_38

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  • DOI: https://doi.org/10.1007/11739685_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33584-9

  • Online ISBN: 978-3-540-33585-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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