On the Properties and Applications of Inconsistent Neighborhood in Neighborhood Rough Set Models

Rough set theory is an important branch of data mining and granular computing, among which neighborhood rough set is presented to deal with numerical data and hybrid data. In this paper, we propose a new concept called inconsistent neighborhood, which extracts inconsistent objects from a traditional neighborhood. Firstly, a series of interesting properties are obtained for inconsistent neighborhoods. Specially, some properties generate new solutions to compute the quantities in neighborhood rough set. Then, a fast forward attribute reduction algorithm is proposed by applying the obtained properties. Experiments undertaken on twelve UCI datasets show that the proposed algorithm can get the same attribute reduction results as the existing algorithms in neighborhood rough set domain, and it runs much faster than the existing ones. This validates that employing inconsistent neighborhoods is advantageous in the applications of neighborhood rough set. The study would provide a new insight into neighborhood rough set theory.