Information Technology Reference
In-Depth Information
We notice that the structure of multidimensional data model is consistent
with the needs of granular structure. A multidimensional data model includes
multiple dimensions, and each dimension includes multiple levels of abstraction.
So each dimension in a multidimensional data model corresponds to a view with
multiple levels of granularity in granular structures. Thus, we will represent a
problem from multiview and multilevel by a multidimensional data model, which
use multidimensional structure to organize data and express the relationships
among data. This representation will facilitate the process of problem solving.
Moreover, concept hierarchy and multidimensional data model can not only to
elicit the content of knowledge, but also its structure.
Granular structures provide descriptions of a system or a problem under con-
sideration. Yao [23] pointed out that granular structures may be accurately de-
scribed as a multilevel view given by a single hierarchy and a multiview under-
standing given by many hierarchies. But he didn't mention how to organize these
multiple hierarchies as an organic whole.
In what follows, we will present multidimensional data model representation
of granular structures through an example.
Example 1.
Representing granular structures of the following problem by a
multidimensional data model, where the problem is provided by table 1.
This problem is provided by a table, where every column represents a par-
ticular view of the problem. So every column can be represented by a concept
hierarchy, as shown in figure 1, figure 2, and figure 3. So this problem can be
represented as a multidimensional data model by organizing these concept hier-
archies as an organic whole, as shown in figure 5. The objects in cells of data
cube as in figure 5 are satisfy properties determined by corresponding coordi-
nate. Or we can say that the objects in cells of data cube is the extension of
a concept, and the intension of the concept is designated by coordinate of the
corresponding cell.
We can obtain the multidimensional data model representation of table 1 as
figure 6 by combining table 1 and granular structure illustrated as figure 5. Or in
other words, we can obtain multidimensional data model as figure 6 by loading
data in table 1 to granular structure as figure 5. For example, the object 4
,
5
,
10
in data cube possesses the properties 'A2', 'B1' and 'C2' simultaneously, that
is, these objects possess properties as 'Low education', work in 'Enterprises' and
'Low income'.
For a given table, we can generalize its every attribute to a concept hierar-
chy tree, and organize these concept hierarchy trees as a multidimensional data
model. In essence, the multidimensional structure of this multidimensional data
model is the granular structure hid in the given table. Thus a given table can be
generalized to multiple tables with different degrees of abstraction by combining
this table and granular structures hid in it. These tables with different degree of
abstraction is the basis of structured problem solving and structured information
processing.
