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

Abstract

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 the Hadamard integral inequality for Sugeno integral from 1-convex functions (ordinary convex functions) to r-convex functions. We present a geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.