Fuzzy neighborhood covering for three-way classification

Neighborhood Covering (NC) is the union of homogeneous neighborhoods and provides a set-level approximation of data distribution. Because of the nonparametric property and the robustness to complex data, neighborhood covering has been widely used for data classification. Most existing methods directly classify data samples according to the nearest neighborhoods. However, the certain classification methods strictly classify the uncertain data and may lead to serious classification mistakes. To tackle this problem, we extend traditional neighborhood coverings to fuzzy ones and thereby propose a Three-Way Classification method with Fuzzy Neighborhood Covering (3WC-FNC). Fuzzy neighborhood covering consists of membership functions and forms an approximate distribution of neighborhood belongingness. Based on the soft partition induced by the memberships of fuzzy neighborhood coverings of different classes, data samples are classified into Positive (certainly belonging to a class), Negative (certainly beyond classes) and Uncertain cases. Experiments verify that the proposed three-way classification method is effective to handle the uncertain data and in the meantime reduce the classification risk.