Attribute reduction is a challenging problem in rough set theory, which has been applied in many research fields, including knowledge representation, machine learning, and artificial intelligence. The main objective of attribute reduction is to obtain a minimal attribute subset that can retain the same classification or discernibility properties as the original information system. Recently, many attribute reduction algorithms, such as positive region preservation, generalized decision preservation, and distribution preservation, have been proposed. The existing attribute reduction algorithms for generalized decision preservation are mainly based on the discernibility matrix and are, thus, computationally very expensive and hard to use in large-scale and high-dimensional data sets. To overcome this problem, we introduce the similarity degree for generalized decision preservation. On this basis, the inner and outer significance measures are proposed. By using heuristic strategies, we develop two quick reduction algorithms for generalized decision preservation. Finally, theoretical and experimental results show that the proposed heuristic reduction algorithms are effective and efficient.
A Neighborhood Rough Sets-Based Attribute Reduction Method Using Lebesgue and Entropy Measures