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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.
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