An information fusion approach by combining multigranulation rough sets and evidence theory

Multigranulation rough set (MGRS) theory provides two kinds of qualitative combination rules that are generated by optimistic and pessimistic multigranulation fusion functions. They are used to aggregate multiple granular structures from a set theoretic standpoint. However, the two combination rules seem to lack robustness because one is too relaxed and the other too restrictive to solve some practical problems. Dempster's combination rule in the evidence theory has been employed to aggregate information coming from multiple sources. However, it fails to deal with conflict evidence. To overcome these limitations, we focus on the combination of granular structures with both reliability and conflict from multiple sources, which has been a challenging task in the field of granular computing. We first address the connection between multigranulation rough set theory and the evidence theory. Then, a two-grade fusion approach involved in the evidence theory and multigranulation rough set theory is proposed, which is based on a well-defined distance function among granulation structures. Finally, an illustrative example is given to show the effectiveness of the proposed fusion method. The results of this study will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing.