Chapter 1 . Applications of Fuzzy Logic
7
The normalized values of these indicators for cluster numbers between 4 and 8
and fuzzifier values of 1.3 and 1.6 are presented in Figure 1.1. Five clusters can be
taken as the "optimal" number of clusters for a fuzzifier of 1.3 - whereas a
fuzzifier of 1.6 does not lead to a clear statement.
1
Partition
coefficient
-Entropy
0,8
-Non-fuzzin.
0,7
index
-
Payoff
0,6
.~~
.... '--..._---..-. ..
0,5 l...L.-_ _ - ' - -_ _ - ' -_ _ - ' -_ _ ---'Ll
a
4
5
6
7
8
Nl.I1iJer cf dusters
1
Partition
0,9
coefficient
-0,8
Entropy
-0,7
Non-fuzzin.
index
0,6
-
Payoff
0,5
0,4 CL.... _ _ - - L _ _ ----L _ _ ---' _ _ _ .1U
b
4
5
6
7
8
Nurmer cf dusters
Fig. 1.1. Partition efficiency indicators for fuzzifier values of 1.3 (left) and 1.6
(right) (Friederichs et al. 1996).