Dynamic probabilistic rough sets with incomplete data

Data in real-world applications are typically changing with time and are often incomplete. To address the challenge of processing such dynamic and incomplete data, we propose a model of dynamic probabilistic rough sets with incomplete data. We introduce incremental methods for estimating the conditional probability and present principles for updating probabilistic approximations when adding and removing objects, respectively. Based on the proposed updating strategies, algorithms are designed for dynamically updating probabilistic approximations with incomplete data. We report experimental evaluations of the efficiency and effectiveness of the proposed incremental algorithms for constructing probabilistic rough set approximations in terms of the size of data and updating ratio by comparing with a non-incremental algorithm. The results show that the new algorithms can effectively utilize the previously acquired knowledge, leading to significantly improved performance over a non-incremental algorithm.