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
2021 International Journal of Computational Intelligence Systems  
Keywords Harmonically convex fuzzy interval-valued function Fuzzy interval fractional integral operator Hermite-Hadamard inequality Hermite-Hadamard-Fejér inequality A B S T R A C T 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
more » ... 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-Fejér (H-H Fejér) 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.
doi:10.2991/ijcis.d.210620.001 fatcat:ok5vwwkm6ze73fwsh6oujfiopa