The objective of the current paper is to incorporate new class and concepts convexity Hermite–Hadamard inequality with fuzzy Riemann integral operators because almost all classical single-valued interval-valued convex functions are special cases fuzzy-number valued mappings. Therefore, a nonconvex mapping in environment has been defined; up down h-pre-invex mappings (U.D F-N∙V∙Ms). With help th...