From negative quantum conditional entropy point of view this paper intestigates the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system.

The identity of the results is proved by means of the fundamental quantum conditions.

Reduction method of decision table based on new conditional entropy;

An incremental approach to computation of a core based on conditional entropy;

Rules extraction method of decision tree based on new conditional entropy;

Based on the characteristics of entropy,relevant entropy and condition entropy,a rough granulation approaching variable is added in the rough set theory.

To this issue,the condition entropy is used as heuristic information for reducing the searching room.

Firstly,the paper gives some concept of rough set theory:decision table,indiscernible relation,information entropy and condition entropy.

Researches on the resolution of fast large time step entropy condition scheme;

By means of characteristics and based on initial conservation law, this paper discusses the existence and uniqueness of weak solution, along with its Rankine-Hugoniot and Entropy Condition.

With the help of characteristic analysis,under suitable generalized Rankine-Hugoniot relation and entropy condition,four different structures of Riemann solutions are established uniquely,in which the interactions among delta shock wave,vacuum and contact discontinuity are clarified.