Ostrowski-Sugeno fuzzy inequalities

  • George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Keywords: Sugeno fuzzy, integral, function fuzzy average, deviation from fuzzy mean, fuzzy Ostrowski inequality

Abstract

We present Ostrowski-Sugeno fuzzy type inequalities. These are Ostrowski-like inequalities in the context of Sugeno fuzzy integral and its special properties are investigated. Tight upper bounds to the deviation of a function from its Sugeno-fuzzy averages are given. This work is greatly inspired by [3] and [1].

References

[1] G.A. Anastassiou, Ostrowski type inequalities, Proc. Amer. Math. Soc. 123(1995), 3775-3781.
[2] M. Boczek, M. Kaluszka, On the Minkowaki-Holder type inequalities for generalized Sugeno integrals with an application, Kybernetica, 52(3) (2016), 329-347.
[3] A. Ostrowski, Uber die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10 (1938), 226-227.
[4] E. Pap, Null-Additive Set functions, Kluwer Academic, Dordrecht, 1995.
[5] D. Ralescu, G. Adams, The fuzzy integral, J. Math. Anal. Appl., 75 (1980), 562-570.
[6] M. Sugeno, Theory of fuzzy integrals and its applications, PhD thesis, Tokyo Institute of Technology (1974).
[7] Z. Wang, G.J. Klir, Fuzzy Measure Theory, Plenum, New York, 1992.
Published
2020-01-20
How to Cite
Anastassiou, G. A. (2020). Ostrowski-Sugeno fuzzy inequalities. CUBO, A Mathematical Journal, 21(3), 29–38. https://doi.org/10.4067/S0719-06462019000300029