Abstract
To create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex FIVFs) which are known as (p, J)-convex FIVFs and to establish Jensen, Schur and Hermite-Hadamard type inequalities for (p, J)-convex FIVFs using fuzzy order relation. The Kulisch-Miranker order relation, which is based on interval space, is used to define this fuzzy order relation level-wise. Additionally, we have demonstrated that, as special examples, our conclusions encompass a sizable class of both new and well-known inequalities for (p, J)-convex FIVFs. We offer helpful examples that demonstrate the theory created in this study's application. These findings and various methods might point the way in new directions for modeling, interval-valued functions and fuzzy optimization issues.