Abstract: Half P-sets (half packet sets) are a set pair composed of internal P-set XF(internal packet set XF)and finite general set X,or (XF,X) is Half P-sets. It has internal dynamic characteristic. Using Half P-sets for rejecting noise data and getting target data,the recursion-rejection method of noise data by supplementing attributes was put forward in this paper. Some concepts were presented such as the noise data, the noise data integration,F-data core. The recursion method and the recuision structure about the generation of the noise data and the generation of F-data were given. The relation theorem between the noise data integration and F-data core was given as well as the dependence and identification theorems of F-data, the recursion-rejection theorems of the noise data. hhe identification criterion and the recursion-rejection criterion for the noise data were provided as well as the applicatin of recursion-rejection for the noise data. Half P-sets are not only a new study branch of theory and application about P-set but also a new mathematical method for researching information systems which have internal dynamic characteristic.

Key words: Half P-sets, Noise data, Noise data integration,F-data core, Recursion-rejection criterion, Application