Information Technology Reference
In-Depth Information
concept of Q using knowledge
P
. Thus the parameter
P
(Q) can be viewed as the
degree of dependency between knowledge
P
and
Q
.
11.3 Decision Logic
Rough set theory defines a basic framework to understand and handle knowledge
using the concept of approximation space. Considering the implementation of
algorithms, it is especially suitable to handle information presented in the form of
data tables, which is called information systems or knowledge representation
systems. This representation systems have many advantages, such as its vivacity.
It can also be viewed as an assembly of propositions about reality and
consequences, thus can be processed by logic tools. This is the motivation of this
section.
11.3.1
Formal Definition of Decision Table
The formal definition of knowledge representation system is
S
=(
U, A
), where
U
is the finite set universe of discussion and
A
denotes the attribute set which is
non-empty and finite.
This definition of knowledge representation systems can easily be
implemented using tables. The tabular representation of knowledge can be
viewed as a special formal language which uses symbols to represent equivalence
relations. In the data table of a knowledge representation system, columns denote
attributes and rows denote objects (such as states or processes), whereas each
row denotes a piece of information about the object. Data tables can be obtained
through observation and measurement.
For each attribute subset
B
⊆
A
, we can define an indiscernible binary relation
IND(
B
), that is
IND(
)∈U
2
, for each
)}. (11.9)
Apparently, IND(B) is an equivalence relation, b∈B, and IND(B)=∩IND(b).
Each subset B⊆A is called as an attribute. When there is only one element in
B, B is called to be original, or complex otherwise. Attribute B can be viewed as
a name of knowledge expressed by equivalence relations, called as marked
attribute. The elementary category including object x and attribute B⊆A is
expressed by a set pair (attribute, value), denoted as {b, b(x)}
b∈B
.
There is a one to one relation between knowledge base and knowledge
representation system, which is determined by the isomorphic of attribute and its
B
)={(
x,y
b
∈
B
,
b
(
x
)=
b
(
y
