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clusters does not necessarily pose any problem. However, for the inspection of the
resulting model this means higher complexity, less transparency, and possibly
wrong conclusions about the characteristics of the system.
Numerical Data
Selection of model structure
( no. of Input-output )
Neuro-fuzzy / fuzzy
clustering based initial rule-
based fuzzy model
Similarity based rule-base
simplification
Fuzzy model evaluation
Accepted final
model
Figure 7.2. Flow chart of transparent fuzzy modelling scheme
Furthermore, in the modelling approach proposed in Figure 7.2, the aggregation
of similar fuzzy sets to a certain degree will correct for bias introduced by having
too many clusters, making the modelling less sensitive to the determination of the
correct number of clusters.
7.4 Similarity Between Fuzzy Sets
The definition of similarity concept between the fuzzy sets depends on their
context. The concept of similarity has been defined, in our case, as the degree to
which the fuzzy sets are equal. For instance, the fuzzy sets F 1 (slow) and F 2 (fast)
in Figure 7.3(a) have exactly the same (triangular) shape, but clearly represent two
distinct concepts, because they are representatives of slow and fast speeds
respectively.
Fuzzy Set
F4
Fuzzy Set
(Low)
F3
Fuzzy Set
Slow
F1
Fuzzy Set
Fast
F2
Temperature
Speed
Figure 7.3(a). Dissimilar fuzzy sets
Figure 7.3(b). Similar fuzzy sets
 
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