In this paper, we defined the fuzzy upper, fuzzy lower, and fuzzy boundary sets of a rough fuzzy set λ in a fuzzy approximation space ( X , R ). Based on λ and R , we introduced the fuzzy ideal approximation interior operator intlambda R and the fuzzy ideal approximation closure operator cl λ R $\text {cl}_{\lambda }^{R}$ . We joined the fuzzy ideal notion with the fuzzy approximation spaces, and then introduced the fuzzy ideal approximation closure and interior operators associated to a rough fuzzy set λ . Fuzzy ideal approximation connectedness and the fuzzy ideal approximation continuity between fuzzy ideal approximation spaces are introduced.

中文翻译：

---

具有模糊理想的模糊粗糙集

在本文中，我们在模糊逼近空间 ( X , R ) 中定义了粗糙模糊集 λ 的模糊上、下和模糊边界集。基于 λ 和 R ，我们引入了模糊理想逼近内部算子 intlambda R 和模糊理想逼近闭包算子 cl λ R $\text {cl}_{\lambda }^{R}$ 。我们将模糊理想概念与模糊逼近空间结合起来，然后引入了与粗糙模糊集 λ 相关联的模糊理想逼近闭包和内部算子。介绍了模糊理想逼近连通性和模糊理想逼近空间之间的模糊理想逼近连续性。