A First Course in FUZZY and NEURAL CONTROL

8.4. IDENTIFICATION OF TRASH IN COTTON 265

Layer 5: The single node in this layer is afixed node labeled

P

,which

computes the overall output as the summation of all incoming signals:

overall output =O 5 =

X

i

wbifi =

P

Piwifi

iwi

The constructed adaptive network is functionally equivalent to a Sugeno

fuzzy model. It is important to note that the structure of this adaptive

network is not unique. For instance, Layers 3 and 4 can be combined to

obtain an equivalent network with only 4 layers. By the same notion, the

weight normalization can be performed in the last layer.

∏

∏

N

N

∑

A 1

A 2

B 1

B 2

w 1 w 1

f

w 2 w 2

x

wf (^11)
y wf (^22)
x y
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
xy

A 1

A 2

B 1

B 2

X

X

Y

x y Y

w 1

w 2

faaxay 10 =+^111 + 21

faaxay 20 =+^212 + 22

f wfwfww

wfwf

= ++

=+

11 2 2

12

11 2 2

(a)

(b)

Figure 8.12.
(a) A two-inputfirst-order Sugeno model with two rules
(b) The equivalent ANFIS architecture
The extension from the Sugeno ANFISto Tsukamoto ANFIS is straightfor-
ward, where the output for each rule (fi,i=1, 2 ) is induced jointly by a