In this paper, the concept of intuitionistic fuzzy mapping as a gen- eralization of fuzzy mapping is presented, and its' relationship with intuitionis- tic fuzzy relations is derived. Moreover, some basic operations of intuitionistic fuzzy mappings are dened, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebra with respect to these operations. Af- terwards, the Atanassov's operator is applied to intuitionistic fuzzy mappings and the corresponding properties are examined. Finally, the decomposition and representation theorems of intuitionistic fuzzy mappings are established.