Information Technology Reference
In-Depth Information
P-positive region of
, and a
set composed by the objects which can be correctly classified into the
equivalence classes of U/Q. The positive region of a set X relative to an
equivalence relation P is the lower approximate of
Q
is the knowledge expressed by
U/P
in universe
U
). The concept of P-
positive region of Q is to deal with the problem, and the objects in the
equivalence classes of Q (viewed as decision attributes) can be classified by the
equivalence classes of P (viewed as condition attributes).
Definition 11.9
X
P*(
X
Suppose P and Q are the family set of equivalence relations on
U, and R
∈
P. If
POS
IND(P)
(IND(Q))=POS
IND(P-{R})
(IND(Q))
then relation
, or Q-irreducible
otherwise. If every relation R in family set P is Q-irreducible, then P is called as
independent relative to Q, or dependent otherwise.
R
is called as Q-reducible in family set
P
Definition 11.10
S
⊆
P is called as Q-reduct of P, iff S is the Q-independent
family subset of P, and POS
S
(Q)=POS
P
(Q); The set of all the Q-irreducible
elementary relations in P is called as Q-core of P, denoted as CORE
Q
(P).
It is easy to see that, when P=Q, above definition is same as the definition
introduced in section 11.2.1.
The following theorem is the extension of theorem 11.1.
Thoerem 11.12
The Q-core of family set P is equal to the intersection of all Q-
reducts, that is
REDQ(P) (11.4)
where REDQ(P) is the family set of all Q-reducts of P.
COREQ(P)=
ŝ
Assume that
P
and
Q
are family sets of equivalent relations (knowledge), the
P
-positive region of Q is the set of all objects that can be classified into the
concept of knowledge Q using knowledge P. If the whole knowledge P is
necessary to categorize objects into the concept of Q, then knowledge P is called
Q-independent. The Q-core of knowledge P is the essence of knowledge P, which
cannot be removed, to maintain the ability of categorizing objects to the concept
of Q. That is, removing any part of the Q-core knowledge will affect the ability
of categorizing objects to the concept of Q. The Q-reduct of knowledge P is some
kind of minimal subset of knowledge P which has the same ability as knowledge
P
to categorize objects to the concept of Q. Note that, knowledge
P
may have
