Efficient updating rough approximations with multi-dimensional variation of ordered data

Ordered data widely exists in practical problems. Dominance-based Rough Set Approach (DRSA) is an effective mathematical tool to obtain approximations of concepts and discovery knowledge from ordered data. In this paper, we focus on the dynamic DRSA for the multi-dimensional variation of an ordered information system, and propose a novel incremental simplified algorithm which can efficiently update approximations of DRSA when objects and attributes increase simultaneously. Most of existing algorithms can efficiently deal with the single-dimensional variation of an information system. However, multi-dimensional variations often occur in real dynamic data. That is, the object set, the attribute set or attribute values of an information system often vary simultaneously. Although we can directly use the definitions of approximations, or integrate some single-dimensional incremental algorithms to cope with multi-dimensional variations, this always results in complex algorithm architectures and a large amount of inefficient computation. In our works, by simplifying traditional definitions of DRSA and employing the incremental learning strategy, we develop an algorithm to neglect unnecessary parameters and avoid much redundant computation. Then, we present two different storage schemes for our proposed algorithm to solve the problem of memory consumption. Finally, a series of experiments are conducted to evaluate its efficiency. Experimental results clearly show that for the two-dimensional variation of objects and attributes in an ordered information system, our proposed algorithm is much faster not only than the non-incremental algorithm based on traditional definitions, but also than the integration of two single-dimensional incremental algorithms.