In this paper, we mainly extend entropy and subsethood from intuitionistic fuzzy sets to general interval-valued intuitionistic fuzzy sets, propose a definition of entropy and subsethood , offer a function of entropy and construct a class of subsethood function. Then from discussing the relationship between entropy and subsethood, we know that while choosing the subsethood, we can get some kinds of function of entropy based on subsethood. Our work is also applicable to practical fields such as: neural networks, expert systems, and other.