Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 233

9. Discovery of Positive and NegativeRules 235

Fig. 9.1. Illustration of focusing mechanism.

9.3 Definition of Rules

9.3.1 Rough Sets

In the following sections, we use the following notation introduced by Grzymala-
Busse and Skowron [9.8], based on rough set theory [9.5]. These notations are
illustrated by a small data set shown in Table 9.1, which includes symptoms
exhibited by six patients who complained of headache.
Let U denote a nonempty finite set called the universe and A de-
note a nonempty, finite set of attributes, i.e., a : U A,

where V a is called the domain of a, respectively. Then a decision table
is defined as an information system, A =(U, A

→ V a for a ∈

∪{ d } ). For example,

Table 9.1 is an information system with U = { 1, 2, 3, 4, 5, 6 } and A =

{ age, location, nature, prodrome, nausea, M1 } and d = class.Forlocation ∈

A, V location is defined as { occular, lateral, whole } .

Table 9.1. Anexample of a data set.
No. ge Location Nature Prodrome Nausea M1 Class

1 -59 occular persistent no no yes m.c.h.

2 -49 whole persistent no no yes m.c.h.

3 40-49 lateral throbbing no yes no migra

4 -49 whole throbbing yes yes no migra

5 -49 whole radiating no no yes m.c.h.

6 -59 whole persistent no yes yes psycho

M1: tenderness of M1; m.c.h.: muscle
contraction headache; migra: migraine; psycho:
psychological pain.