Abstract
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.
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G.A. Anastassiou, Fractional Ostrowski-Sugeno Fuzzy univariate inequalities (2018). Submitted
G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G.A. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, New York, 2011)
G.A. Anastassiou, Advances on Fractional Inequalities (Springer, New York, 2011)
G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities (Springer, New York, 2016)
M. Boczek, M. Kaluszka, On the Minkowaki-Hölder type inequalities for generalized Sugeno integrals with an application. Kybernetica 52(3), 329–347 (2016)
J.A. Canavati, The Riemann-Liouville integral. Nieuw Archief Voor Wiskunde 5(1), 53–75 (1987)
K. Diethelm, The Analysis of Fractional Differential Equations, 1st edn., Lecture notes in mathematics, vol 2004 (Springer, New York, 2010)
A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)
E. Pap, Null-Additive Set functions (Kluwer Academic, Dordrecht, 1995)
D. Ralescu, G. Adams, The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)
M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. thesis, Tokyo Institute of Technology (1974)
Z. Wang, G.J. Klir, Fuzzy Measure Theory (Plenum, New York, 1992)
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Anastassiou, G.A. (2019). Fractional Ostrowski–Sugeno Type Fuzzy Integral Univariate Inequalities. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_16
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DOI: https://doi.org/10.1007/978-3-030-04287-5_16
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