P-sets, Inverse P-sets and the Intelligent Fusion-filter Identification of Information
P-集合，逆P-集合与信息智能融合-过滤辨识

P-sets(Packet sets) are obtained by embedding the dynamic characteristics into the finite general set X and improving it,which have the dynamic characteristic.P-sets are a set-pair composed of internal P-set X(internal packet set X) and outer P-set XF(outer packet set XF),or(XF,X) is P-sets.Under a certain condition,P-sets can be restored to finite general set X.P-sets are the mathematical expression of one class dynamic system.Inverse P-sets(inverse packet sets) are obtained by P-sets,which have also dynamic characteristic.Inverse P-sets have the opposite mathematics structure to P-sets,which are a set pair composed of inernal inverse P-set F(internal inverse packet set F) and outer inverse P-set(outer inverse packet set),or(F,) is inverse P-sets.Under a certain condition,inverse P-sets can be restored to finite general set X.Inverse P-sets are the mathematical expression of the other class dynamic system.P-reasoning(packet reasoning) is the dynamic reasoning generated by P-sets,and inverse P-reasoning(inverse packet reasoning) is the dynamic reasoning generated by inverse P-sets.By intersecting and infiltrating P-sets,inverse P-sets,P-reasoning,inverse P-reasoning with information fusion,the intelligent fusion-filter identification theory of information and its application study were given.The paper gave the structures,the separations and the equivalence class characteristics of P-sets and inverse P-sets,P-information fusion and inverse P-information fusion,the reasoning discovery,fusion measure,filter-identification of P-information fusion and inverse P-information fusion,the application of the intelligent fusion-filter identification of information.P-sets and inverse P-sets are new theories and methods of studying information fusion theory and application.