Intuitionistic fuzzy number (IFN) is an effective tool for dealing with the uncertain information, and it has been applied to various fields. According to IFNs, the intuitionistic fuzzy calculus has been developed, which can effectively integrate the continuous uncertain information. Series in intuitionistic fuzzy environment is a part of the intuitionistic fuzzy calculus theory, of which core idea is limit. However, the order used in the existing limit theory is not the one used in intuitionistic fuzzy calculus, causing the separation of the limit theory and intuitionistic fuzzy calculus. Thus, series in intuitionistic fuzzy environment is not closely related to the intuitionistic fuzzy calculus. In order to solve the above problem, we construct the related theories. There are mainly the following three aspects: (1) the limit theory including the sequence limit and the function limit is studied based on the new order. (2) we re-examine the numerical series according to the new tool of researching IFNs: the basis and the coordinates. (3) we discuss the function series and put forward the uniform convergence in intuitionistic fuzzy environment.

中文翻译：

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直觉模糊环境中基于新阶的级数

直觉模糊数（IFN）是处理不确定信息的有效工具，已被应用到各个领域。根据干扰素，已经开发出直觉模糊演算，可以有效地整合连续的不确定信息。直觉模糊环境中的级数是直觉模糊演算理论的一部分，其核心思想是极限。但是，现有极限理论中使用的顺序不是直觉模糊演算中使用的顺序，从而导致极限理论和直觉模糊演算分离。因此，直觉模糊环境中的级数与直觉模糊演算并不紧密相关。为了解决上述问题，我们构建了相关理论。主要有以下三个方面：（1）基于新的顺序研究了包括序列极限和功能极限的极限理论。（2）我们根据研究IFN的新工具重新检查了数值序列：基础和坐标。（3）讨论了函数级数，并提出了直觉模糊环境下的一致收敛性。