Hierarchy On Multigranulation Structures: A Knowledge Distance Approach

In this paper, a knowledge distance approach is proposed to study the hierarchy under the frame of multigranulation. In our approach, the finest granulation structure is considered as the frame of reference, and then a knowledge distances algebraic lattice is constructed. Through such algebraic lattice, a partial order is derived, which can be used to characterize the finer or coarser relationships among multigranulation structures. It is also shown that the uncertainty measurements are monotonic in terms of the obtained partial order.