Matrix-based local multigranulation reduction for covering decision information systems

Abstract

Attribute reduction has become an essential step in pattern recognition and machine learning tasks. As an extension of the classical rough set, the covering rough set has garnered considerable attention in both theory and application. A matrix-based method for computing local covering optimistic approximation sets and local optimistic multigranulation reductions based on covering rough set in covering decision information systems (CDISs) is proposed in this paper. Firstly, we introduce a matrix representation along with its associated operations to compute the local covering optimistic approximation sets and the local positive regions of the CDISs. Subsequently, local optimistic discernibility matrices and local optimistic discernibility functions are constructed for the CDISs. By performing disjunction and conjunction operations on these local optimistic discernibility matrices, all local optimistic multigranulation reductions of the CDISs can be accurately obtained. In addition, an algorithm is developed using the local optimistic discernibility matrix to compute a suboptimal minimal local optimistic multigranulation reduction. Finally, to verify the effectiveness and feasibility of the proposed method, numerical experiments are conducted on 6 UCI datasets.