Topological reduction approaches for relation decision systems

In this study, we use topological methods to investigate attribute reduction problems for relation decision systems. We propose the notions of topological consistent and inconsistent relation decision systems. Then, we propose the concept of the consistent topological reduction of topological consistent relation decision systems. To enlarge the scope of application, we define the general topological reduction of relation decision systems, which is a further generalization of consistent topological reduction. Moreover, we develop corresponding reduction algorithms for these two types of reductions. To demonstrate that our algorithms cannot be unified by the general reduction algorithm, we discuss the relationship between the consistent topological reducts and the reducts identified by the general reduction algorithm. We conduct numerical experiments on 11 UCI datasets to verify our theoretical results. The experimental results demonstrate that the proposed reduction algorithms are effective and practicable.& COPY; 2023 Elsevier Inc. All rights reserved.