Properties of Convex Fuzzy-Number-Valued Functions on Harmonic Convex Set in the Second Sense and Related Inequalities via Up and Down Fuzzy Relation

Abstract

In this paper, we provide different variants of the Hermite–Hadamard (H⋅H) inequality using the concept of a new class of convex mappings, which is referred to as up and down harmonically s-convex fuzzy-number-valued functions (UDH s-convex FNVM) in the second sense based on the up and down fuzzy inclusion relation. The findings are confirmed with certain numerical calculations that take a few appropriate examples into account. The results deal with various integrals of the 2ρσρ+σ type and are innovative in the setting of up and down harmonically s-convex fuzzy-number-valued functions. Moreover, we acquire classical and new exceptional cases that can be seen as applications of our main outcomes. In our opinion, this will make a significant contribution to encouraging more research.

Keywords

• up and down harmonically <i>s</i>-convex fuzzy-number-valued function in the second sense
• Hermite–Hadamard inequality
• Hermite–Hadamard–Fejér inequality