Biomedical Engineering Reference
In-Depth Information
Figure 3. FDT for example data set with two MFs
describing each condition attribute
“If T1 = H and T3 = H then C = L, with truth
level 1.000”.
Following this exposition of one of the fuzzy
decision rules constructed from the analysis, its
presence as a path in tree structure shown in
Figure 3. Indeed, further inspection of Figure
3 can familiarize the reader with the tree based
representation of all the fuzzy decision rules
constructed
FUzzy DECISION TREE ANALySES
OF TWO bIOLOGy PRObLEMS
The main thrust of this chapter is the demonstra-
tion of the previously described FDT technique
employed in two animal biology based studies. The
first application of the FDT technique investigates
the prediction of the age of abalones through an
analysis of their physical measurements (Waugh,
1985). The second application considers the torpor
bouts of hibernating Greater Horseshoe bats, based
on associated characteristics (Park
et al
., 2000).
In each study the FDTs constructed should be
viewed as attempting to exposit the relationship
between the condition attributes describing the ob-
jects and the decision attribute which categorises
them in some way. Due to the availability of the
respective data, from these two applications are
contrasting, which further exposits the possible
use of FDT based analyses.
are; T3
L
;
S
(T1
H
∩ T3
L
, C
L
) = 0.400
and
S
(T1
H
∩
T3
L
, C
H
) =
0.600
; T3
H
:
S
(T1
H
∩ T3
H
, C
L
) =
1.000
and
S
(T1
H
∩ T3
H
, C
H
) = 0.143. With each suggested
classification path, the largest subsethood value is
below (for
S
(T1
H
∩ T3
L
, C
H
) = 0.600) and
above
(
S
(T1
H
∩ T3
H
, C
L
))
the defined truth level thresh-
old, hence only one of the paths becomes a leaf
node (T1 = H then T3 = H), the other path would
need checking for further augmentation with the
last of the attributes T2. The construction process
continues as before for this last check, the resultant
FDT in this case is presented in Figure 3.
The tree structure in Figure 3 clearly demon-
strates the visual form of the results using FDTs.
Each path (branch) from the root node (using T1)
describes a fuzzy decision rule using conditions
from the condition attributes to a specified deci-
sion class. Only shown in each leaf node box is
the truth level associated with the highest subset-
hood value to the represented decision category.
There are four levels of the tree showing the use
of all the considered condition attributes. There
are four leaf nodes which each have a defined
decision rule associated with them. For example,
the rule
R4
can be written as,
FDT Analysis of Abalones
The first FDT analysis concerns the subject of
abalones, in particular, the prediction of their
age using information regarding physical mea-
surements (the data is included in the UCI data
repository, with the original source is from Waugh,
1995). As a classification problem, there continues
to be concerns on the inaccuracy or bias associ-
ated with current techniques used to obtain age
and growth data for abalones, such as age from
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