If si < x then divide the two adjacent data into
different groups;
else put them into the same group.
After the above operation, we can obtain the
result formed as (y:, Rj), meaning that the ith out-
put data will be clustered into the Rj, where
Ri means the jth produced fuzzy region.
Example 4. Assume a is set at 0.8. The training
examples are then grouped as follows:
Substep (le): Determine membership jimctions of
the output space. For simplicity, triangle member-
ship functions are used here for each linguistic
variable. A triangle membership function can be
defined by a triad (a, b,c) as Fig. 5 shows (not
necessarily symmetric).
In this substep, we propose a heuristic method
for determining these three parameters. First,
we assume that the center point b lies at the
center-of-gravity of the group. Next, we try to
find the membership values of two boundary train-
ing outputs in the group, where “boundary training
outputs” mean the minimum and maximum out-
puts in that group. The two end points a and c
of the output membership function can then be
found through the extrapolation of b and the
two boundary training outputs. The following
four procedures are then used to achieve this
purpos