Since the algorithm of attribute reduction based on positive region is based on the thought of lower approximation, it just considers the right distinguished samples. Using the thought of upper approximation and the concept of neighborhood information granule, the distinguished object set with its basic characteristics was designed and analyzed, then the new attribute importance measurement based on distinguished object set and heuristic attribute reduction algorithm was proposed. The proposed algorithm considered both the relative positive region of information decision table and the influence on boundary samples when growing condition attributes. The feasibility of the algorithm was discussed by instance analysis, and the comparative experiments on UCI data set with attribute reduction algorithm based on positive region were carried out. The experimental results show that the proposed attribute reduction algorithm can get better reduction, and the classification precision of sample set can remain the same or has certain improvement.
Focusing on the underdeveloped robustness when the existing extended rough set model encounters the noise for the incomplete information system, the necessity of adjusting the size of basic knowledge granule as well as introducing the relative degree of misclassification was analyzed. Then the Variable Precision Rough Set model based on Variable-Precision Tolerance Relation (VPRS-VPTR) was established on the basis of the object connection weight matrix, which was proposed according to the lack probability of system attribute value. Moreover, the properties of the VPRS-VPTR model were discussed, the classification accuracy under the basic knowledge granule size and the relative degree of misclassification was analyzed, the corresponding algorithm was depicted and the time complexity analysis was given afterwards. The experimental results show that the VPRS-VPTR model has higher classification accuracy compared with some other research about the expanded rough set, and the change trend of the classification accuracy is similar for the train set and the test set of several groups of incomplete data sets in UCI database. It proves that the proposed model is more precise and flexible, and the algorithm is feasible and effective.
In order to evaluate a systems security and predict the attack actions, an attack model based on system states aggregation was presented. In the model, the threat was abstracted as the aggregation of the systems states, and the attack process was depicted as the change of the system states aggregation. A method of detecting network attacks and early warning using the model was also described. Based on the model, an early warning prototype was implemented. Our experiment shows that the prototype is able to detect attack processes effectively and predict the possible risk level the system will reach.