Fractional $q$-calculus is considered to be the fractional analogs of $q$-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) $q$-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving $\hslash$-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF $q$-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.

分数$q$-微积分被认为是分数类似物$q$-结石。在本文中，模糊区间值黎曼-刘维尔分数（RLF）$q$-引入积分运算符。还有 Hermite–Hadamard (HH) 类型和 HH–Fejér 不等式的新模糊变体，涉及$\hslash$-凸模糊区间值函数（FIVF），通过利用 RLF 来呈现$q$-不可缺少的。研究结果不仅概括了现有文献的研究结果，而且为FIVF不平​​等问题的研究奠定了坚实的基础。此外，为了验证我们的理论发现，提供了数值示例和必要的图形说明。