Active attack and defense on attribute reduction with fuzzy rough sets

Attribute reduction based on dynamically updated datasets in fuzzy rough sets plays a significant role in dealing with the uncertainty of time-evolving updated data. However, current research on attribute reduction lacks theoretical mechanisms to actively distinguish and defend against malicious interference in datasets. Aiming at this problem, an attribute reduction update framework with defense is proposed for dynamic datasets with adversarial attack. In this framework, an adversarial attack model is presented to select the optimal attacked attributes and construct the adversarial samples to generate the attack datasets. Based on this, a defense model is designed by constructing defense samples to avoid attacks. Firstly, the key identification sample pairs that determine the discernibility of the minimal element subset are defined, which are then used to define the attack target candidate set and construct adversarial samples. To alter the discernibility attributes of the key discernibility sample pairs, the attribute significance degree with attack preference is defined to select the unimportant attributes to attack. Then, the attack model is designed to select the optimal attacked candidate subset and generate the attack dataset. Targeting the attack strategy, defense samples for both the optimal attacked attribute subset and the useless attribute set are constructed to generate the defense matrix and defense datasets. Finally, a unified update strategy for attribute reduction after attack and defense is proposed to induce the updated reduct. Numerical experiments verify the rationality and effectiveness of the framework proposed in this paper based on the success rate of attack and defense, as well as the classification results.