Rough set analysis of graphs

Abstract

Relational data has become increasingly important in decision analysis in recent years, and so mining knowledge which preserves relationships between objects is an important topic. The graph can represent the knowledge which contains objects and relationships between them. Rough set theory provides an effective tool for extracting knowledge which does not preserve the data on relationships between objects. But it is not sufficient to extract the knowledge containing the data on relationships between objects. In order to extend the application scope and enrich the theoretical content of the rough set theory, it is essential to develop a rough set analysis of graphs. The extension is important because graphs play a crucial role in social network analysis. In this paper, the rough set analysis of graphs based on general binary relations is investigated. We introduce three types of approximation operators of graph: vertex graph approximation operators, edge graph approximation operators, and graph approximation operators. Relationships between approximation operators of graph and approximation operators of set are presented. Then we investigate the approximation operators of graph within constructive and axiomatic approaches.