Hermite–Hadamard-Type Inequalities for Coordinated Convex Functions Using Fuzzy Integrals

Abstract

In this paper, some estimates of third and fourth inequalities in Hermite–Hadamard-type inequalities for coordinated convex functions are proved using the non-additivity of the integrals and Fubini’s theorem for fuzzy integrals. That is, the results are obtained in the fuzzy context and using the Lebesgue measure. Several examples are provided on how to evaluate these estimates in order to illustrate the obtained results.

Keywords

• fuzzy measure
• Sugeno integral
• Hermite–Hadamard’s inequality
• Fubini’s theorem