Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities
Gul Sana, Muhammad Bilal Khan, Muhammad Aslam Noor, Pshtiwan Othman Mohammed, Yu‐Ming Chu
Abstract
It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator. With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejr (H-H Fejr) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.