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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.
Sana et al. (2021) studied this question.