Fuzzy Decision Trees - Data Mining with Decision Trees: Theory and Applications - page 225

Chapter 14
Fuzzy Decision Trees
14.1 Overview
There are two main types of uncertainty in supervised learning: statistical
and cognitive. Statistical uncertainty deals with the random behavior of
nature and all techniques described in previous chapters can handle the
uncertainty that arises (or is assumed to arise) in the natural world
from statistical variations or randomness. While these techniques may be
appropriate for measuring the likelihood of a hypothesis, they say nothing
about the meaning of the hypothesis.
Cognitive uncertainty, on the other hand, deals with human cognition.
Cognitive uncertainty can be further divided into two sub-types: vagueness
and ambiguity. Ambiguity arises in situations with two or more alternatives
such that the choice between them is left unspecified. Vagueness arises when
there is a diculty in making a precise distinction in the world.
Fuzzy set theory, first introduced by Zadeh in 1965, deals with cognitive
uncertainty and seeks to overcome many of the problems found in classical
set theory. For example, a major problem in the early days of control theory
is that a small change in input results in a major change in output. This
throws the whole control system into an unstable state. In addition, there
was also the problem that the representation of subjective knowledge was
artificial and inaccurate.
Fuzzy set theory is an attempt to confront these diculties and in this
chapter we present some of its basic concepts. The main focus, however, is
on those concepts used in the induction process when dealing with fuzzy
decision trees. Since fuzzy set theory and fuzzy logic are much broader than
the narrow perspective presented here, the interested reader is encouraged
to read [ Zimmermann (2005) ] .
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