Multi-scale covering rough sets with applications to data classification

Abstract

When facing with a complex problem, one often needs to consider dealing with it at what level of granularity. Multi-scale knowledge representation provides us an opportunity to analyze problems from different granularity. However, as well as traditional rough sets model, most of existing multi-scale rough set models are based on partitions generated from equivalence relations, which limits their application in real data. In this paper, we set forth a new data analysis model with multi-scale coverings by extending partitions to coverings. To this end, a new type of decision tables, i.e., multi-scale covering decision tables are formalized to deal with knowledge representation under multi-scale framework. Optimal scale selection for consistent and inconsistent covering decision tables are then proposed to obtain acceptable decisions under coarser scales. Furthermore, the acquisition of optimal rules with higher accuracy and covering rate are discussed. Extensive experiments on some real-world data sets are set up to examine the effectiveness and feasibility of the proposed model. Experimental results show that the multi-scale covering theory gives a new way to enhance the generalization ability of the classification model.