The intuitionistic fuzzy set (A-IFS) was introduced by Atanassov to generalize the concept of Zadeh’s fuzzy set. The basic elements of an A-IFS are the intuitionistic fuzzy numbers (IFNs). In this paper, we deal with the intuitionistic fuzzy set with the help of Einstein operations. First we introduce some operations of A-IFS, such as the Einstein sum, Einstein product, Einstein scalar multiplication and Einstein exponentiation, and redefine two new and important operation as Einstein subtraction and Einstein division. Then we investigate the limit, continuity and derivatives of intuitionistic fuzzy functions (IFFs) based on the Einstein operations. Furthermore and what is more, some infinite and definite integrals for the IFFs are discussed importantly, and an aggregation method based on the definite integral was introduced to solve some actual decision making problems, which focus on the original data and obtain better overall evaluations in information aggregation.

中文翻译：

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基于爱因斯坦运算的直觉模糊微积分

Atanassov 引入直觉模糊集 (A-IFS) 来推广 Zadeh 模糊集的概念。A-IFS 的基本元素是直觉模糊数 (IFN)。在本文中，我们借助爱因斯坦运算处理直觉模糊集。首先介绍A-IFS的一些运算，如爱因斯坦求和、爱因斯坦乘积、爱因斯坦标量乘法和爱因斯坦取幂，并重新定义爱因斯坦减法和爱因斯坦除法这两个新的重要操作。然后我们研究了基于爱因斯坦运算的直觉模糊函数（IFFs）的极限、连续性和导数。此外，重要的是讨论了IFFs的一些无限定积分，