New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals

Numerous applications of the theory convex and nonconvex mapping exist in fields applied mathematics engineering. In this paper, we have defined a new class functions which is known as up down pre-invex (pre-incave) fuzzy number valued mappings (F-N-V?Ms). The well-known Hermite–Hadamard (????????)-type related inequalities are taken into account work. We extend mileage further using Riemann integrals pre-invexity. Additionally, by imposing some light restrictions on mappings, introduced two significant classes pre-invexity (pre-incavity), referred to lower upper mappings. By these definitions, amassed large both established novel exceptional situations that serve implementations key findings. To support validity inclusion relations put out research, also provide few examples numbers