Weighted Multi-granulation Containment Neighborhood Rough Set Model

Abstract

Neighborhood rough set theory is an important method for dealing with uncertainty, fuzziness and undefined objects, and neighborhood rough set theory based on binary relation is studied by scholars a lot. However, most of the current research is used to deal with equivalent binary relations or other binary relations with stringent condition, which has been unable to meet the rapid development of data. This paper proposes a new multi-granulation rough set that can deal with general binary relations based on the C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</inf> neighborhoods, and verifies its related properties. At the same −time, it has richer meanings through weighted methods. Theoretical analysis and practical examples show that this rough set has better ability to process data. Finally, a weighted attribute reduction algorithm is designed based on the significant function under the general binary relation. The experimental results show that this rough set can handle complex data well. The research in this paper develops the theory of classical rough sets, and provides a theoretical basis for the knowledge acquisition of information systems under the general binary relation.