Riemann–Liouville Fractional Integral Inequalities for Generalized Harmonically Convex Fuzzy-Interval-Valued Functions

Abstract

Abstract The framework of fuzzy-interval-valued functions (FIVFs) is a generalization of interval-valued functions (IVF) and single-valued functions. To discuss convexity with these kinds of functions, in this article, we introduce and investigate the harmonically $$\mathsf{h}$$ h -convexity for FIVFs through fuzzy-order relation (FOR). Using this class of harmonically $$\mathsf{h}$$ h -convex FIVFs ( $$\mathcal{H}-\mathsf{h}$$ H - h -convex FIVFs), we prove some Hermite–Hadamard (H⋅H) and Hermite–Hadamard–Fejér (H⋅H Fejér) type inequalities via fuzzy interval Riemann–Liouville fractional integral (FI Riemann–Liouville fractional integral). The concepts and techniques of this paper are refinements and generalizations of many results which are proved in the literature.

Keywords

• Harmonically-convex fuzzy-interval-valued function
• Hermite
• Hadamard inequality
• Hermite
• Hadamard
• Fejér inequality