Khan, Muhammad BilalSantos-García, G.Budak, HüseyinTreanta, SavinSoliman, M.S.2023-07-262023-07-2620232473-6988https://doi.org/10.3934/math.2023374https://hdl.handle.net/20.500.12684/12704To 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. © 2023, American Institute of Mathematical Sciences. All rights reserved.en10.3934/math.2023374info:eu-repo/semantics/openAccess(p,J)-convex fuzzy-interval-valued functionFuzzy Riemann integralHermite-Hadamard type inequalityHermite-Hadamard-Fejér type inequalityJensen type inequalitySchur type inequalityArticle83743774702-s2.0-85147022369WOS:000923463800010Q2Q1