Dynamic variable precision rough set approach for probabilistic set-valued information systems

Set-valued information systems are important type of data tables in many real applications, where the attribute values are described by sets to characterize uncertain and incomplete information. However, in some real situations, set-values may be depicted by probability distributions, which results in that the traditional tolerance relation based on intersection operation could not reasonably describe the indiscernibility relation of objects. To address this issue, we introduce the concept of probabilistic set-valued information systems (PSvIS), and present the extended variable precision rough set model (VPRS) based on the λ-tolerance relation in terms of Bhattacharyya distance. Considering the features of information systems will evolve over time in a dynamic data environment, it will lead to the change of information granulation and approximation structures. A matrix representation of rough approximation is presented based on two matrix operators and two vector functions in PSvIS. Then incremental mechanisms by the utilization of previously learned approximation results and region relation matrices for updating rough approximations are proposed, and the corresponding algorithms are developed and analyzed. Experimental results show that the proposed algorithms outperform the static algorithms and related incremental algorithms while inserting into or removing from attributes in PSvIS.