Rough set analysis of graphs

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. Graphs can represent the knowledge which contains objects and relationships between objects. Rough set theory provides an effective tool for extracting knowledge, 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 rough set theory, it is essential to develop a rough set analysis of graphs. This 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 graphs: vertex graph approximation operators, edge graph approximation operators, and graph approximation operators. Relationships between approximation operators of graphs and approximation operators of sets are presented. Then we investigate the approximation operators of graphs within constructive and axiomatic approaches.