<p>Superquadratic function is a generalization of convex functions. Results based on superquadratic functions are more refined than the results obtained using the notion of convexity. This work aims to provide a new class of superquadratic functions called superquadratic fuzzy-interval-valued function (superquadrtic $ F_{I.V.F} $) and demonstrate its properties using fuzzy order relations. In the space of fuzzy intervals, this relation is also termed as the Kulisch-Miranker order relation defined on such a space level-wise. By leveraging the definition and features of superquadrtic $ F_{I.V.F} $, we come up with improved integral inequalities such as Hermite-Hadamard (H.H) and Jensen type for superquadrtic $ F_{I.V.F} $. Furthermore, we offer fractional representation of inequalities of H.H's types for superquadrtic $ F_{I.V.F} $ with respect to fuzzy interval Riemann-Liouville fractional integral operators. These findings are further validated through specific numerical examples and graphical illustrations, which demonstrate the practical relevance and applicability of the results. We have no doubt that these results will open new avenues for researchers to further explore the notion of superuadraticity.</p>