The Exposition of Fuzzy Decision Trees and Their Application in Biology - Advancing Artificial Intelligence Through Biological Process Applications - page 384

Table 3. Information on the initial intervalisation of the AGE decision attribute

Description (AGE - years) Low (L) Medium (M) High (H)

Interval L ≤ 8.5 (333) 8.5 < M ≤ 11.5 (334) 11.5 < H (333)

Mean 6.937 9.823 14.634

the shell layers, prompting consideration of alter-
native techniques (see for example the decision
presented in Gurney , 2005).
Here, a sample of 1000 abalones was analysed,
which offered a balance in numbers over the three
age categories considered on them. In this study,
the three ordered categories of age are described
as (in linguistic terms); low (L), medium (M) and
high (H), see Table 3.
In Table 3, the intervals shown define the ma-
jority support sub-domains of the AGE linguistic
terms, L, M and H, where the values in brackets
are the numbers of abalones included in each
interval (supporting the previously stated bal-
anced numbers desired with each category). Also
shown are the means of the AGE values of the
abalones included in each interval. The interval
details shown in Table 3 are used to construct the
respective MFs that define each of the linguistic
terms L, M and H, in a fuzzy sense, so used as
the necessary defining values [α j, 1 , α j, 2 , α j, 3 , α j, 4 ,
α j, 5 ] for each term, previously defined.
To demonstrate the assignment of values
to the defining values, with the linguistic term
AGE = M (2 nd interval) its mean value is 9.823
years, hence α 2,3 = 9.823. The neighbouring
defining values, α j, 2 and α j, 4 , around α j, 3 are the

left and right boundary values of that interval,
respectively (so here they are α 2,2 = 8.5 and α 2,4
= 11.5). The final outer defining values, α j, 1 and
α j, 5 , are the middle (modal) defining values of its
neighbouring intervals (so here α 2,1 = 6.937 and
α 2,5 = 14.634). The left and right end intervals
need special consideration, often necessitating the
use of −∞ and ∞, respectively. In the case of the
constructed intervals for the AGE attribute given
in Table 3, Figure 4 elucidates the sequence of
linear piecewise (triangular) MFs which describe
the linguistic terms associated with the AGE
decision attribute.
The MFs presented in Figure 4 clearly show
how the defining values have been employed, as
described earlier, for example the MF m AGE,M (⋅)
has the associated defining values [6.937, 8.5,
9.823, 11.5, 14.634].
Attention then turns to the description of the
condition attributes used to describe the abalones
and which may be used in the prediction of the
abalones' respective AGE values (when using
FDTs), see Table 4.
Included in the eight condition attributes de-
scribed in Table 4 are seven continuous attributes,
which quantify different variations on their size
and weight of the abalone, and a nominal attribute,

Figure 4. Membership functions of the linguistic terms, L, M and H, describing the linguistic