Separation of dynamic data and recovery of P-abnormal data

The main purpose of this paper is to study abnormal data whose data elements are increased and decreased simultaneously in data transmission. By using a new mathematic model of P-sets which has dynamic characteristics, this paper proposes the concepts of \( \bar{F} \)-abnormal data, \( F \)-abnormal data, \( (\bar{F},F) \)-abnormal data and P-abnormal data, including \( \bar{F} \)-lost data and \( F \)-intrusive data. P-abnormal data consists of \( \bar{F} \)-abnormal data, \( F \)-abnormal data and \( (\bar{F},F) \)-abnormal data. Based on research for P-abnormal data, the paper also gives a separation algorithm for dynamic data by using P-sets and the set difference operation on general set. By using this algorithm, information systems can determine whether the detected data is standard. If the data is not standard, it can be separated into \( \bar{F} \)-abnormal data or \( F \)-abnormal data. In addition, this paper gives a method for recognition of P-abnormal data and two methods for recovery of P-abnormal data. Finally, this paper provides an application for the separation of dynamic data and recovery of P-abnormal data. The study shows that the separation algorithm is a new mathematical tool. It can be applied in data processing which has the internal dynamic characteristics, outer dynamic characteristics or both dynamic characteristics simultaneously.