Intuitionistic fuzzy set (A-IFS) introduced by Atanassov, a generalized form of fuzzy sets, is a useful tool to deal with vagueness and ambiguity. Each element of an A-IFS is called an intuitionistic fuzzy value, based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. However, the existing study only discusses the one-variable IFC, in order to enrich the theory of the IFC; in this paper, we put forward the intuitionistic fuzzy multiple definite integrals (IFMDI). We first define some concepts related to the IFMDI, based on which we reveal the relationships between the IFMDI and the intuitionistic fuzzy definite integrals. After that we investigate the basic properties of the IFMDI in detail, and finally, we apply the knowledge of abstract algebra to construct some isomorphic mappings, based on which, we interpret the reason why there are some parallel properties between the additive IFMDI and the multiplicative IFMDI.

中文翻译：

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直觉模糊微积分和同构映射的多重定积分

Atanassov 引入的直觉模糊集 (A-IFS) 是模糊集的一种广义形式，是处理模糊性和歧义性的有用工具。A-IFS 的每个元素称为直觉模糊值，最近基于该值提出了直觉模糊演算 (IFC)。然而，现有的研究只讨论了单变量IFC，以丰富IFC的理论；在本文中，我们提出了直觉模糊多重定积分（IFMDI）。我们首先定义了一些与IFMDI相关的概念，在此基础上我们揭示了IFMDI与直觉模糊定积分之间的关​​系。之后我们详细研究了IFMDI的基本性质，最后，我们应用抽象代数的知识构造了一些同构映射，在此基础上，