Yong-hong Shen - School of Mathematics and Statistics, Tianshui Normal Univer- sity, Tianshui ۷۴۱۰۰۱, People's Republic of China
Fa-xing Wang - Tongda College, Nanjing University of Posts and Telecommunica- tions, Nanjing, ۲۱۰۰۴۶, People's Republic of China
Wei Chen - School of Information, Capital University of Economics and Business, Beijing, ۱۰۰۰۷۰, People's Republic of China

In this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. Moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. Afterwards, the Atanassov'soperator is applied to intuitionistic fuzzy mappings and thecorresponding properties are examined. Finally, the decompositionand representation theorems of intuitionistic fuzzy mappings areestablished.

Truncation projection, Intuitionistic fuzzy mapping, Truncation map- ping, Decomposition theorem, Representation theorem