Derivative and Differential Operations of Intuitionistic Fuzzy Numbers

The innovative idea of Atanassov's intuitionistic fuzzy sets (A-IFSs) is to get a more comprehensive and detailed description of the ambiguity and uncertainty by introducing a membership function and a nonmembership function. Each element in an A-IFS is expressed by an ordered pair, which is called an intuitionistic fuzzy number (IFN). In this paper, we first describe the change values of IFNs when considering them as variables and classify these change values based on the basic operations for IFNs. Second, we depict the convergences of sequences of IFNs by the subtraction and division operations. Moreover, we develop some intuitionistic fuzzy functions (IFFs) and study in detail their continuities, derivatives, and differentials.