Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 231

9.Discovery of PositiveandNegativeRules
from Medical Databases Based on Rough
Sets

Shusaku Tsumoto
Department of Medical Informatics, Shimane University, School of Medicine,
89-1 Enya-cho Izumo City, Shimane 693-8501, Japan;
email: [e-mail]

One of the important problems in rule-induction methods is that extracted
rules do not plausibly represent information on experts' decision processes. To
solve this problem, the characteristics of medical reasoning are discussed. The
concept of positive and negative rules is introduced. Then, for induction of
positive and negative rules, two search algorithms are provided. The proposed
rule-induction method is evaluated on medical databases. The experimental
results show that the induced rules correctly represent experts' knowledge,
and several interesting patterns are discovered.

9.1 Introduction

Rule-induction methods are classified into two categories, induction of de-
terministic rules and of probabilistic ones [9.4], [9.5], [9.7], [9.10]. On one
hand, deterministic rules are described as if-then rules, which can be viewed
as propositions. From the set-theoretical point of view, a set of examples
supporting the conditional part of a deterministic rule, denoted by C,isa
subset of a set whose examples belong to the consequence part, denoted by
D. That is, the relation C

D holds and deterministic rules are supported
only by positive examples in a data set. On the other hand, probabilistic
rules are if-then rules with probabilistic information [9.10]. When a classical
proposition will not hold for C and D, C is not a subset of D but closely
overlapped with D. That is, the relations C

⊆

δ
will hold in this case, where the threshold δ is the degree of closeness of over-
lapping sets, which will be given by domain experts. (For more information,
see Section 9.3.) Thus, probabilistic rules are supported by a large number of
positive examples and a few negative examples. The common feature of both
deterministic and probabilistic rules is that they deduce their consequence
positively if an example satisfies their conditional parts. We call the reasoning
by these rules positive reasoning.
However, medical experts use not only positive reasoning but also neg-
ative reasoning for selection of candidates, which is represented as if-then
rules whose consequences include negative terms. For example, when a pa-
tient who complains of headache does not have a throbbing pain, migraine
should not be suspected with a high probability. Thus, negative reasoning

∩ D = φ and | C ∩ D | / | C |≥