A New Measure for Determining the Equivalent Symmetry of Decomposed Subsystems from Large Complex Cyber–Physical Systems

In this paper, we propose a new consistency measurement for classification rule sets that is based on the similarity of their classification abilities. The similarity of the classification abilities of the two rule sets is evaluated though the similarity of the corresponding partitions of the feature space using the different rule sets. The proposed consistency measure can be used to measure the equivalent symmetry of subsystems decomposed from a large, complex cyber–physical system (CPS). It can be used to verify whether the same knowledge is obtained by the sensing data in the different subsystems. In the experiments, five decision tree algorithms and eighteen datasets from the UCI machine learning repository are employed to extract the classification rules, and the consistency between the corresponding rule sets is investigated. The classification rule sets extracted from the use of the C4.5 algorithm on the electrical grid stability dataset have a consistency of 0.88, which implies that the different subsystems contain almost equivalent knowledge about the network stability.