Multi-granular mining for boundary regions in three-way decision theory

In three-way decision theory, all samples are divided into three regions: a positive region, a negative region, and boundary regions. A lack of detailed information may make a definite decision impossible for samples in boundary regions, and hence the third non-commitment option is used. Reducing boundary regions is a new problem. In this paper, the multi-granular three-way decision (MGTD) algorithm is presented to reduce boundary regions. At the beginning of the multi-granular process, samples are divided using the covering algorithm, which does not need a threshold. Then pairs of heterogeneous points (HPs) are defined in boundary regions to obtain diversity information. This detailed information is used to define attribute subsets. Eventually, boundary regions are further investigated using multiple-views of granularity. Each view corresponds to an attribute subset. Experiments have shown that the MGTD algorithm is beneficial for reducing boundary regions and improving classification precision in most cases.