Line Integrals of Intuitionistic Fuzzy Calculus and Their Properties

Atanassov's intuitionistic fuzzy set (A-IFS) is a powerful tool to handle uncertainty and vagueness in real life. The basic elements of an A-IFS are intuitionistic fuzzy values, based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. However, to date, there is no investigation for intuitionistic fuzzy line integrals (FLIs), which are very important for further developing IFC. In this paper, we propose the IFLIs and give their concrete values. After that, we investigate a series of basic properties of the IFLIs in detail, moreover, in order to show the utility of the proposed IFLIs, we offer an example, and finally, we discuss the relationships among the additive IFLI, the multiplicative IFLI, and the intuitionistic fuzzy aggregation operators.