Fuzzy Prediction Model in Privacy Protection: Takagi–Sugeno Rules Model via Differential Privacy

Rule-based fuzzy models have modular architectures and come with well-developed design methodologies such that they can build accurate models with good interpretabilities in system modeling. However, a large amount of private data needs to be used for statistical analysis and forecasting in rule-based fuzzy models. The purpose of this study is to build an intelligent model with high accuracy and versatility under the premise of data privacy and model security. To mitigate the risk of malicious attacks on privacy data during the analysis process, we have employed highly regarded differential privacy techniques to devise a novel rule-based fuzzy modeling approach. We propose a function approximation mechanism to reconstruct the objective function and add a perturbation mechanism to the objective function in the Takagi–Sugeno rules model. Taking into account the delicate balance between data privacy and utility, we have innovatively introduced a Takagi–Sugeno rule-based model based on differential privacy. This model is applicable to both linear and nonlinear systems, offering protection to sensitive data privacy and model security within the system. We investigate the relationship between the interpretability of the model and the degree of privacy protection. By constructing a reasonable rule base, we achieve higher accuracy than other system modeling methods based on differential privacy. This article compares the influence of the number of rules on differential privacy and considers the algorithm performance under various noise distributions. It is shown that the Takagi–Sugeno rules model based on differential privacy has a strong ability to predict and analyze data.