Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 238

240 Shusaku Tsumoto

R A

D

Fig. 9.6. Venn diagram of negative rules.

¬ [M1=yes] ∧¬ [nausea = no] →¬ m.c.h.

In summary, a negative rule is defined as:

[a j = v k ] κ [a j =v k ] (D)=1.0,
where D denotes a set of samples that belong to a class d. Figure 9.6 shows
the Venn diagram of a negative rule. As shown in this figure, it is notable
that this negative region is the “positive region” of “negative concept.”
Negative rules should also be included in a category of deterministic rules,
because their coverage, a measure of negative concepts, is equal to 1.0. It is
also notable that the set supporting a negative rule corresponds to a subset
of negative region, which is introduced in rough sets [9.5].
In summary, positive and negative rules correspond to positive and neg-
ative regions defined in rough sets. Figure 9.7 shows the Venn diagram of
those rules.

∧ j ¬ [a j = v k ] →¬ d s.t. ∀

Fig. 9.7. Venn diagram of defined rules.