Characterizing Hierarchies on Covering-Based Multigranulation Spaces

Hierarchy plays a fundamental role in the development of the Granular Computing(GrC). In many practical applications, the granules are formed in a family of the coverings, which can construct a Covering-based Multigranulation Space(CBMS). It should be noticed that the hierarchies on Covering-based Multigranulation Spaces has become a necessity. To solve such problem, the concepts of the union knowledge distance and the intersection knowledge distance are introduced into the CBMS, which can be used to construct the knowledge distance lattices. According to the union knowledge distance and the intersection knowledge distance, two partial orderings can be derived, respectively. The example shows that the derived partial orderings can compare the finer or coarser relationships between two different Covering-based Multigranulation Spaces effectively. The theoretical results provide us a new way to the covering based granular computing.