A Hadamard-type inequality for fuzzy integrals based on r-convex functions

• Published in: Soft computing (Berlin, Germany) Vol. 20; no. 8; pp. 3117 - 3124
• Main Authors: Abbaszadeh, Sadegh, Eshaghi, Madjid
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Convex analysis; Engineering; Foundations; Hypotheses; Inequality; Integrals; Mathematical Logic and Foundations; Mechatronics; Probability; Robotics; Upper bounds; Seminormed Sugeno integral; convex function; The Hadamard inequality; Sugeno integral

In this paper, it is shown that the Hadamard integral inequality for r -convex functions is not satisfied in the fuzzy context. Using the classical Hadamard integral inequality, we give an upper bound for the Sugeno integral of r -convex functions. In addition, we generalize the results related to t...