Abstract
Intuitionistic fuzzy set (IFS), introduced by Atanassov (1986), is the generalization of Zadeh’s fuzzy set. The basic element of IFS is an ordered pair called intuitionistic fuzzy number, based on which, Lei and Xu originally introduced the intuitionistic fuzzy function (IFF) and then developed the derivatives and differentials of IFFs. In the paper, we first define the binary intuitionistic fuzzy numbers (BIFNs) and put forward their operational principles. Then, we discuss the limit and the continuity of sequences of BIFNs. In addition, we study the continuities, the partial derivatives and the complete differentials of the intuitionistic binary fuzzy functions and then generalize the aforementioned definitions and theorems to derive the counterparts of the multivariate intuitionistic fuzzy functions.
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