Information Technology Reference
In-Depth Information
b
0
∨
b
2
→
d
1
e
1
a
1
→
d
2
e
2
a
2
b
1
→
d
1
e
2
For Table 11.12, we can generate its decision rules attached with rough
operators directly as follows.
a
1
b
0
c
2
→
0.5
d
2
e
0
a
0
b
1
c
1
→
0.5
d
1
e
2
a
1
b
0
c
2
→
0.5
d
0
e
1
a
0
b
1
c
1
→
0.5
d
0
e
1
At last, combine the decision algorithms generated from totally consistent and
totally
inconsistent
decision
tables,
and
then
the
decision
algorithm
corresponding to the original inconsistent decision table is got.
11.5 Extended Model of Rough Sets
Comparing with other method processing imprecise or uncertain information,
basic rough set theory has its advantages. However, it still has some shortages. At
present, most of the successful applications are based on the extension of basic
rough set theory from various aspects. Under the assumption that known objects
in universe have all necessary knowledge, basic rough set theory is a tool
processing fuzziness and uncertainty. It is in essence a kind of tri-value logic
(positive region, boundary region and negative region).
The main problems in basic rough set theory can be summarized as follows:
(1) Poor ability in processing the fuzziness of original data;
(2) Too simple description of rough set's boundary region;
(3) With basic rough set based methods, when the information is incomplete,
objects are classified into a special class, and usually the class is
determined. However, in real applications, a mass of objects need to be
classified with given error ratios. Basic rough set theory cannot deal with
these cases.
In the research of rough set theory, researchers have already proposed many
extended models, such as variable precision rough set (VPRS) models, some
rough set based nonmonotonic models, and the models integrating rough set
theory and evidence theory. In the following, we will focus on some of them.
