Pre-Invexity and Fuzzy Fractional Integral Inequalities via Fuzzy Up and Down Relation

The symmetric function class interacts heavily with other types of functions. One these is the pre-invex class, which strongly related to symmetry theory. This paper proposes a novel fuzzy fractional extension Hermite-Hadamard, Hermite-Hadamard-Fejér, and Pachpatte type inequalities for up down fuzzy-number-valued mappings. Using operators, several generalizations have been developed, where well-known results fit as particular cases. Additionally, some non-trivial examples are included support discussion applicability key findings. approach appears trustworthy effective dealing various nonlinear problems in science engineering. findings general may constitute contributions complex waveform