Hypergraph-based attribute reduction of formal contexts in rough sets

The process of attribute reduction is a critical aspect of rough set theory as applied to data analysis. Several methods for attribute reduction have been outlined in previous studies. For instance, hypergraph theory has shed light on this area. However, most existing methods of attribute reduction focus on theories, leading to complexities when searching for attribute reducts due to an absence of visuality. Moreover, although certain existing methods of attribute reduction are used by certain visual methods, such as that of combining hypergraphs, none of them acknowledge the uniqueness of the relationship between hypergraphs and the corresponding information systems. This flaw results in accurate results for a specific information system under consideration in a particular paper, but unreliable results for another system. Consequently, it impedes the promotion of attribute reduction in rough set theory. Thus, investigating a visual method free of this limitation, to accomplish attribute reduction, emerges as a task that requires immediate resolution in rough set theory. This paper addresses this problem for a conventional information system (formal context). First, this paper illustrates the process of constructing a hypergraph from a formal context and vice versa. The two constructions are verified to be unique under isomorphisms. We found that our method exhibits superior time complexity compared to certain methods that constructed basic graphs from certain information systems. Second, under the Pawlak umbrella of classical rough set model for a formal context, this study constructs a family P of equivalence relations on the set of objects. With the aid of a diagram of the relevant hypergraph within the formal context, it presents a method for determining the dispensability of each element in P. Third, guided by the relevant hypergraph of the formal context, an approach for investigating reducts of P and the attribute set is proposed. Compared with certain methods of attribute reduction in rough sets using hypergraphs, the approach proposed in this paper is superior in certain aspects. Finally, the obtained results are verified and demonstrate practical applications through an example of biological classification. The use of hypergraph diagrams in the proposed methodology enhances its visibility, therefore contributing to the enrichment of attribute reduction in rough set theory. This is beneficial for the promotion and application of the resulting achievements.