Fractional Ostrowski–Sugeno Type Fuzzy Integral Univariate Inequalities

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


Here we present fractional univariate Ostrowski-Sugeno Fuzzy type inequalities. These are of Ostrowski-like inequalities in the setting of Sugeno fuzzy integral and its special-particular properties. In a fractional environment, they give tight upper bounds to the deviation of a function from its Sugeno-fuzzy averages. The fractional derivatives we use are of Canavati and Caputo types.


  1. 1.
    G.A. Anastassiou, Fractional Ostrowski-Sugeno Fuzzy univariate inequalities (2018). SubmittedGoogle Scholar
  2. 2.
    G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)CrossRefGoogle Scholar
  3. 3.
    G.A. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, New York, 2011)CrossRefGoogle Scholar
  4. 4.
    G.A. Anastassiou, Advances on Fractional Inequalities (Springer, New York, 2011)CrossRefGoogle Scholar
  5. 5.
    G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities (Springer, New York, 2016)CrossRefGoogle Scholar
  6. 6.
    M. Boczek, M. Kaluszka, On the Minkowaki-Hölder type inequalities for generalized Sugeno integrals with an application. Kybernetica 52(3), 329–347 (2016)Google Scholar
  7. 7.
    J.A. Canavati, The Riemann-Liouville integral. Nieuw Archief Voor Wiskunde 5(1), 53–75 (1987)MathSciNetzbMATHGoogle Scholar
  8. 8.
    K. Diethelm, The Analysis of Fractional Differential Equations, 1st edn., Lecture notes in mathematics, vol 2004 (Springer, New York, 2010)Google Scholar
  9. 9.
    A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)Google Scholar
  10. 10.
    E. Pap, Null-Additive Set functions (Kluwer Academic, Dordrecht, 1995)zbMATHGoogle Scholar
  11. 11.
    D. Ralescu, G. Adams, The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)MathSciNetCrossRefGoogle Scholar
  12. 12.
    M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. thesis, Tokyo Institute of Technology (1974)Google Scholar
  13. 13.
    Z. Wang, G.J. Klir, Fuzzy Measure Theory (Plenum, New York, 1992)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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