Anti-containment and α-anti-containment neighborhoods-based neighborhood rough sets and their classification models in medical application for infectious diseases

Abstract

Uncertainty modeling aims to improve the accuracy and reliability of predictions by identifying and quantifying uncertainties through statistical and analytical methods. In particular, neighborhood rough set models have undergone significant development in the latest medical applications for infectious diseases, and they improve approximation accuracies and achieve risk classifications. However, there is a lack of clear semantic explanation of the existing containment neighborhoods in medical applications, and the corresponding classification methods are relatively simple and lack practicality. In this paper, the systemic $\alpha$-containment, $\alpha$-anti-containment and anti-containment neighborhoods are constructed by semantic analyses of posterior and conditional probabilities, and thus they not only deduce novel neighborhood rough sets but also drive more detailed classification models that can be flexibly applied to different medical scenarios. Firstly, posteriori probabilities and a threshold are introduced to propose the $\alpha$-containment neighborhoods. Then, the $\alpha$-anti-containment and anti-containment neighborhoods are constructed by using conditional probabilities. Accordingly, they can induce new neighborhood rough sets and obtain better approximation accuracies. In addition, the inclusion relationships between the proposed and existing neighborhoods are discussed, and the threshold monotonicity is studied through theoretical analysis and examples. Furthermore, the proposed neighborhoods are employed to classify individuals at some suspected risk of infectious diseases for different application scenarios (such as the transmission research of infected individuals and the tracing of the root causes of infectious diseases), based on the semantic analysis of posterior and conditional probabilities. By flexibly selecting thresholds, the $\alpha$-containment and $\alpha$-anti-containment neighborhoods can deduce more detailed classification models that are more practical for actual needs. Finally, several examples of medical application are implemented to illustrate the advantages of our classification models. The optimal accuracies and threshold monotonicity are validated through datasets experiments, showing that the three proposed classification models are superior to the existing models. Therefore, the whole research is beneficial to the development of neighborhoods, uncertainty modeling and medical applications.