Analysis of superquadratic fuzzy interval valued function and its integral inequalities

What is it about?

This work aims to provide a new class of superquadratic functions called superquadratic fuzzy-intervalvalued function (superquadrtic FI.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 FI.V.F, we come up with improved integral inequalities such as Hermite-Hadamard (H.H) and Jensen type for superquadrtic FI.V.F. Furthermore, we offer fractional representation of inequalities of H.H’s types for superquadrtic FI.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.

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Why is it important?

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.

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