An introduction to the variable neighborhood and the related adaptive determination algorithm

The neighborhood-based multi-granulations rough set (NMGRS) is the latest extended model of the multi-granulations rough set (MGRS), which makes the MGRS can deal with real-value data. As one of the most important parameters, the neighborhood size has a significant impact on attribute reduction. However, the common methods to get a neighborhood size rely on keeping trying different values and experiences. And all the attributes are assigned the same value, which ignores their differences on the distribution and the contribution to the decision. Therefore, this paper proposes a new algorithm which assigns adaptively different attributes different neighborhood sizes (it is defined as the variable neighborhood) according to the data distributions. The minimal between class distances of each attribute is regarded as a very important indicator to form such a neighborhood size. The results of experiments on different types of data sets prove that the proposed algorithm can get a better attribute reduction and further make the NMGRS more pervasive and practical.