LAUSR

The main objective of this study is to introduce new versions of fractional integral inequalities in fuzzy fractional calculus utilizing the introduced preinvexity. Due to the behavior of its definition, the idea of preinvexity plays a significant role in the subject of inequalities. The concepts of preinvexity and symmetry have a tight connection thanks to the significant correlation that has developed between both in recent years. In this study, we attain the Hermite-Hadamard (H⋅H) and Hermite-Hadamard-Fejér (H⋅H Fejér) type inequalities for preinvex fuzzy-interval-valued functions (preinvex F⋅I⋅V⋅Fs) via Condition C and fuzzy Riemann–Liouville fractional integrals. Furthermore, we establish some refinements of fuzzy fractional H⋅H type inequality. There are also some specific examples of the reported results for various preinvex functions deduced. To support the newly introduced ideal, we have provided some nontrivial and logical examples. The results presented in this research are a significant improvement over earlier results. This paper’s awe-inspiring notions and formidable tools may energize and revitalize future research on this worthwhile and fascinating topic.