Incremental updating probabilistic neighborhood three-way regions with time-evolving attributes

Abstract

Neighborhood decision systems (NDSs) are commonly-used systems in real-world applications such as credit scoring. Probabilistic neighborhood rough sets (PNRSs) model, which is a generalized rough set model by combining neighborhood rough sets (NRSs) with probabilistic theory, can efficiently handle numerical data with noise values and allow tolerance of errors. Approximations of a target concept are fundamental and vital notions of the PNRSs, which can induce the certain and uncertain decision rules. Nevertheless, data evolves over time due to dynamic characteristics, especially, the addition of new attributes and the deletion of redundant or irrelevant attributes. Therefore, the potential meaningful knowledge may alter over time accordingly. To improve the efficiency of acquiring decision rules, the three-way regions (i.e., the positive, negative, and boundary regions) of the PNRSs need to be updated in an incremental fashion. To address this issue, two incremental algorithms for updating the three-way regions of each decision class of the PNRSs are investigated from the matrix perspective with time-evolving attributes (namely, adding attributes and deleting attributes). First, a matrix-based characterization of the three-way regions of each decision class of the PNRSs is constructed. Subsequently, considering the variation of the attributes, matrix-based updating mechanisms for relevant matrices are developed by means of the previously calculated information. Furthermore, the incremental algorithms are developed by taking advantage of the matrix-based updating mechanisms. Comprehensive experiments are performed on benchmark UCI data sets, and comparative results demonstrate our proposed algorithms consistently outperform the non-incremental algorithm in terms of computational efficiency.