Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 235

9. Discovery of Positive and NegativeRules 237

Fig. 9.2. Venn diagram of accuracy and coverage.

9.3.3 Probabilistic Rules

By use of accuracy and coverage, a probabilistic rule is defined as:
R α,κ → d s.t. R = ∧ j [a j = v k ],α R (D) ≥ δ α

δ κ .
If the thresholds for accuracy and coverage are set to high values, the mean-
ing of the conditional part of probabilistic rules corresponds to the highly
overlapped region. Figure 9.3 depicts the Venn diagram of probabilistic rules
with highly overlapped region. This rule is a kind of probabilistic proposi-

and κ R (D) ≥

R A

D

R D s t D R D s t D .. .. ( ) ( ) > , , → →

α α

> δ α δ α

R () R ()

κ κ

> > δ κ δ κ

R R

Fig. 9.3. Venn diagram for probabilistic rules.