A general reduction algorithm for relation decision systems and its applications

This paper studies the attribute reduction problem for general relation decision systems. We propose a new discernibility matrix to solve this problem. Combining the discernibility matrix and a recently proposed fast algorithm, we propose a simple and unified attribute reduction algorithm for relation decision systems that is not contingent on the consistency of relation decision systems. We derive the reduction algorithm for the special cases of complete, incomplete, and numerical decision tables. As an application, we transform the attribute reduction of relation decision systems into one for covering decision systems. This gives a convenient and effective reduction algorithm for covering decision systems. The reduction results obtained using University of California Irvine data sets show that the proposed algorithm is simple and efficient. Moreover, the proposed algorithm enables the results of classical attribute reduction approaches to be reinterpreted, giving them far greater unification and generality. (C) 2016 Elsevier B.V. All rights reserved.