It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite–Hadamard inequalities (-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann–Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter and real valued function selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications.

中文翻译：

---

模糊区间分数演算中的新Hermite-Hadamard不等式及相关不等式

众所周知的事实是，不等式已成为使用分数积分的一种非常流行的方法，并且这种方法已成为近年来许多研究背后的驱动力。已经研究了许多形式的不平等，从而导致了不平等理论的新趋势的引入。本文的目的是使用模糊序关系来引入各种类型的不等式。在模糊区间空间上，此模糊顺序关系是逐级定义的。在这种关系的帮助下，首先，我们导出凸模糊区间值函数（凸模糊IVF）的一些离散Jensen和Schur不等式，然后，通过模糊区间Riemann-Liouville分式积分。这些结果是对许多先前已知结果的概括，适当的参数和实值函数的选择可以推导出许多新的结果。我们希望我们的模糊顺序关系结果可以用于评估与实际应用相关的许多数学问题。