The information granulation in discretization

Discretization is a vehicle of abstraction that supports a conversion of clouds of numeric data into more tangible information granules, which can be represented as hyper-boxes in R". A partial ordering of all discretization schemes for a given information table is defined to describe the relative granularity. All discretized tables form a hierarchical structure, representing the information table under different granulation. The granule-based entropy is defined to measure the information change in discretization. With meet and join operations, the partially ordered set becomes a lattice named discretization lattice, which is a Boolean algebra.