In this paper, the concept of intuitionistic fuzzy labelling (IFL) has been introduced. Intuitionistic fuzzy bi-magic labelling (IFBL) and intuitionistic fuzzy anti-magic labelling (IFAL) have been discussed for cycle, star and path graph. Intuitionistic fuzzy sets will be given both degree of membership and degree of non-membership, which are independent of each other to the extent, that their sum is not greater than one. Various types of arcs have been analysed and blank arc has been introduced and also discussed for intuitionistic fuzzy labelling. We also discussed about intuitionistic fuzzy bridge and intuitionistic fuzzy cut-vertices with examples and their properties are studied.
