F-recursive binary tree

P-sets consists of an internal P-set X F and an outer P-set X F and has dynamic characteristics, which result from the internal dynamic characteristics on X F and the outer dynamic characteristics on X F . In order to extend the application of the P-sets, the paper proposes an F-recursive binary tree through applying the dynamic characteristics for the P-set X F . Meanwhile, the paper provides the structures and characteristics for the F -recursive binary tree, including some properties and theorems about the F-recursive binary tree. The paper also gives the method of constructing F-recursive binary tree. The F-recursive binary tree has inward contraction characteristics and recursive characteristics. It can be used many research fields, such as information science and technology, artificial intelligence, knowledge discovery, as well as control theory and control engineering.