Some fuzzy-interval integral inequalities for harmonically convex fuzzy-interval-valued functions

Abstract

It is well-known fact that fuzzy interval-valued functions (F-I-V-Fs) are generalizations of interval-valued functions (I-V-Fs), and inclusion relation and fuzzy order relation on interval space and fuzzy space are two different concepts. Therefore, by using fuzzy order relation (FOR), we derive inequalities of Hermite-Hadamard (H·H) and Hermite-Hadamard Fejér (H·H Fejér) like for harmonically convex fuzzy interval-valued functions by applying fuzzy Riemann integrals. Moreover, we establish the relation between fuzzy integral inequalities and fuzzy products of harmonically convex fuzzy interval-valued functions. The outcomes of this study are generalizations of many known results which can be viewed as an application of a defined new version of inequalities.

Keywords

• harmonically convex fuzzy interval-valued function
• fuzzy-interval integrals
• hermite-hadamard inequality
• hermite-hadamard fejér inequality