科研之友
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摘要
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.
