The Sugeno integral with respect to α-preinvex functions
Jiagen Liao a , Shanhe Wu b , Tingsong Du a,c,∗
Abstract
In this paper, we establish the left hand side of the Hermite–Hadamard inequality for α-preinvex functions, and illustrate that the Hermite–Hadamard inequality for α-preinvex functions is not valid for the Sugeno integral. Moreover, we give several upper bounds for the Sugeno integral related to α-preinvex functions. Some examples are also provided to show the validity of our results.
Keywords: Hermite–Hadamard inequality; Sugeno integral; α-Preinvex function