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Figure 18.9 depicts an example of a fuzzy rule set (seven rules) with Takagi-
Sugeno reasoning for the corresponding non-linear fuzzy model. Our RMSE is now
16.48 and thus slightly better than in the linear case. In this context we operate with
such fuzzy rules as
If
Age
is approx.
A
and
Bmi
is approx.
B
,the
Syst
is approx.
C
and our initial rules are in Table 18.6. Figure 18.10 depicts our non-linear fuzzy
fitting surface.
Table 18.6
Initial fuzzy rules for the model
Syst
vs.
Age
and
Bmi
Rule If
Age
is and
Bmi
is then
Syst
is
1
55.8
21.7
119.6
2
55.8
23.5
138.6
3
63.7
23.2
140.2
4
56.5
24.4
151.0
5
61.9
25.9
165.5
6
57.9
29.9
184.4
7
62.3
31.2
201.4
Fig. 18.9
Tentative fuzzy rules for the fuzzy first-order Takagi-Sugeno model
Syst
vs.
Age
and
Bmi
Thanks for our linguistic approach with fuzzy rules, we may understand better the
interrelationships between the independent and dependent variables. This is essen-
tial particularly in the non-linear models because then corresponding mathematical
resolutions may be much more complicated and inconceivable.