In this paper, we propose a method to construct homeomorphisms from the interior of intuitionistic fuzzy interpretation triangle to the complex plane. Based on such homeomorphisms, we define concepts of pure intuitionistic fuzzy sets and pure intuitionistic fuzzy numbers, and obtain some properties of these new concepts. In addition, we prove that all the pure intuitionistic fuzzy numbers form a field, whose arithmetic operations are given. Finally, we use two numerical examples to show computational skills in such field.