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Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide range of applications. We define a new Hermite–Hadamard inequality for the novel class of coordinated ƛ-pre-invex fuzzy number-valued mappings (C-ƛ-pre-invex F N V M s) and examine the idea of C-ƛ-pre-invex F N V M s in this paper. Furthermore, using C-ƛ-pre-invex F N V M s, we construct several new integral inequalities for fuzzy double Riemann integrals. Several well-known results, as well as recently discovered results, are included in these findings as special circumstances. We think that the findings in this work are new and will help to stimulate more research in this area in the future. Additionally, unique choices lead to new outcomes. [ABSTRACT FROM AUTHOR]

In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann's integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ -Godunova–Levin convex fuzzy number mappings, to derive Ostrowski's and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results. [ABSTRACT FROM AUTHOR]