A picture fuzzy set (PFS) is an augmentation of Atanassov’s intuitionistic fuzzy set (IFS). The PFS-based models are useful in the circumstances when we face uncertain and vague information, especially in the case when we need more answers of the form “indeed,” “avoid,” “no,” and “refusal.” It has been considered as an essential tool to deal with unsure data during an investigation. In this manuscript, we explore the idea of a picture fuzzy near-ring (PFNR) and a picture fuzzy ideal (PFI) of a near-ring (NR). We illustrate some basic properties such as union, intersection, homomorphic image, and preimage of PFIs of a NR. Furthermore, there is discussion about the direct product of PFIs of a NR.

中文翻译：

---

环附近的图像模糊理想

图片模糊集（PFS）是Atanassov直觉模糊集（IFS）的增强。基于PFS的模型在我们面临不确定和模糊的信息的情况下很有用，尤其是当我们需要更多形式为“确实”，“避免”，“否”和“拒绝”的答案时。它被认为是处理调查期间不确定数据的必要工具。在本手稿中，我们探讨了图像模糊近环（PFNR）和图像近似理想（PFI）的概念。我们说明了一些基本属性，例如NR的PFI的并集，交集，同态图像和前像。此外，还有关于NR的PFI的直接乘积的讨论。