A Hypergraph-Based Approach to Attribute Reduction in an Incomplete Decision System

Attribute reduction has been demonstrated to be an effective approach for addressing fuzziness and uncertainty in data analysis, especially for data dimension reduction. As an extension of graphs, hypergraphs have been established by prior research as a potent mathematical framework for attribute reduction in decision systems. However, current studies rarely explore the integration of hypergraphs and rough set theories for attribute reduction in incomplete decision systems. To bridge this theoretical gap, this paper proposes a novel hypergraph-based attribute reduction method for incomplete decision systems through a matrix. Firstly, we introduce two types of construction methods for the characteristic matrices of a hypergraph, and the characteristic matrix decomposition relationship between them is examined. Moreover, some features in hypergraphs including transversal are systematically investigated via these characteristic matrices. Secondly, using the characteristic matrices of the hypergraphs derived from an incomplete information system, a hypergraph-based method is developed for the process of attribute reduction in incomplete information systems via a discernibility matrix. Finally, we discuss the attribute reduction method of incomplete decision systems, and establish a new judgment method for the attribute reduction in incomplete decision systems through the constructed characteristic matrices of hypergraphs.