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constructed from atomic formula by only logic connective
. A concept space
CDS
is then referred to as the conjunctively definable space, which is a sub-
space of the definable space
DS
. Similarly, a concept space is referred to as
a disjunctively definable space if the atomic formulas are connected by logic
disjunctive
∧
.
In [29], we discuss the complete concept space for classification tasks us-
ing granular network concepts. The immediate result is that a classification
task can be understood as a search of the distribution of classes in a granule
network defined by the descriptive attribute set. The analysis shows that the
complexity of the search space of a consistent classification task is not polyno-
mially bounded. This can be extremely complex especially when the number
of possible values of attributes are large, let alone continuous. This forces us
to use heuristic algorithms to quickly find solutions in a constrained space.
Indeed, the existing heuristic algorithms perform very well. Each of them can
be understood as a particular heuristic search within the granule network.
∨
4.2 Rule Interestingness Evaluation on the Three-Layered
Framework
Traditionally, when we talk about evaluating the usefulness and interesting-
ness of discovered rules and patterns, we talk about many measures based on,
for example, information theory and measurement theory. Thus, the study of
interestingness evaluation is a theory-oriented study referring to the categories
in Sect. 2.
With respect to the framework, in the philosophical layer, quantitative
measures can be used to characterize and classify different types of rules. In
the technique layer, measures can be used to reduce search space. In the appli-
cation layer, measures can be used to quantify the utility, profit, effectiveness,
or actionability of discovered rules.
From the existing studies, one can observe that rule evaluation plays at
least three different types of roles:
i. In the data mining phase, quantitative measures can be used to reduce the
size of search space. An example is the use of well-known support measure,
which reduces the number of itemsets that need to be examined [1].
ii. In the phase of interpreting mined patterns, rule evaluation plays a role in
selecting the useful or interesting rules from the set of discovered rules [17,
18]. For example, the confidence measure of association rules is used to
select only strongly associated itemsets [1, 9].
iii. In the phase of consolidating and acting on discovered knowledge, rule
evaluation can be used to quantify the usefulness and effectiveness of dis-
covered rules. Many measures such as cost, classification error, and classi-
fication accuracy play such a role [4].
To carry out the above three roles, many measures have been proposed
and studied. We need to understand that measures can be classified into two
