Advertisement

Multidimensional Ostrowski–Sugeno Type Fuzzy Integral Inequalities

  • George A. Anastassiou
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 190)

Abstract

Here we present multivariate Ostrowski–Sugeno Fuzzy type inequalities. These are multivariate Ostrowski-like inequalities in the context of Sugeno fuzzy integral and its special properties. They give tight upper bounds to the deviation of a multivariate function from its Sugeno-fuzzy multivariate averages. It follows [3].

References

  1. 1.
    G.A. Anastassiou, Multivariate Ostrowski type inequalities. Acta Math. Hung. 76(4), 267–278 (1997)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G.A. Anastassiou, Quantitative Approximations (Chapman & Hall/CRC, Boca Raton, 2001)zbMATHGoogle Scholar
  3. 3.
    G.A. Anastassiou, Multivariate Ostrowski-Sugeno fuzzy inequalities (2018). SubmittedGoogle Scholar
  4. 4.
    M. Boczek, M. Kaluszka, On the Minkowaki-Hölder type inequalities for generalized Sugeno integrals with an application. Kybernetica 52(3), 329–347 (2016)zbMATHGoogle Scholar
  5. 5.
    A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)CrossRefGoogle Scholar
  6. 6.
    E. Pap, Null-Additive Set Functions (Kluwer Academic, Dordrecht, 1995)zbMATHGoogle Scholar
  7. 7.
    D. Ralescu, G. Adams, The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Sugeno, Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)Google Scholar
  9. 9.
    Z. Wang, G.J. Klir, Fuzzy Measure Theory (Plenum, New York, 1992)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

Personalised recommendations