Dynamic maintenance of updating rough approximations in interval-valued ordered decision systems

In the new era of information society, dynamic data is common and widely applied in many fields. To save the computing time of upper and lower approximations in rough methods, it is wise to study the incremental methods of calculating approximations and construct the incremental algorithms. In this study, we mainly focus on maintaining approximations dynamically in interval-valued ordered decision systems when the feature set and sample set increase or decrease, respectively. Firstly, the dominance relation on interval-valued ordered decision system are discussed. The two notions of interval dominance degree and interval overlap degree (denoted as IDD and IOD respectively) are introduced to describe the preference relation between interval values. Then, the incremental updating rules of approximations for four circumstances, namely adding attributes, removing attributes, adding objects, and removing objects, are obtained based on the matrix expression of approximations and dominated sets. Furthermore, the incremental algorithms are derived accordingly. By using six preprocessed data sets from UCI repository, a series of evaluations and comparisons are made on the calculation time of static algorithm and incremental algorithms. From these comparative experiments, the effectiveness and superiority of the proposed dynamic algorithms could be verified.