Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 236

238 Shusaku Tsumoto

tion with two statistical measures, which is an extension of Ziarko's variable
precision model (VPRS) [9.15]. 1
It is also notable that both a positive rule and a negative rule are defined
as special cases of this rule, as shown in the next sections.

9.3.4 Positive Rules

A positive rule is defined as a rule supported by only positive examples, the
classification accuracy of which is equal to 1.0. It is notable that the set
supporting this rule corresponds to a subset of the lower approximation of a
target concept, which is introduced in rough sets [9.5]. Thus, a positive rule
is represented as:

∧ j [a j = v k ], α R (D)=1.0
. Figure 9.4 shows the Venn diagram of a positive rule. As shown in this
figure, the meaning of R is a subset of that of D. This diagram is exactly
equivalent to the classic proposition R

R → d s.t. R =

d.
In the preceding example, one positive rule of m.c.h. (muscle contraction
headache) is:

→

[nausea = no] → m.c.h. α =3/3=1.0.

This positive rule is often called a deterministic rule. However, we use the
term, positive (deterministic) rules, because a deterministic rule supported
only by negative examples, called a negative rule, is introduced in the next
section.
1 This probabilistic rule is also a kind of rough modus ponens [9.6].

D

R A

Fig. 9.4. Venn diagram of positive rules.