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y
…
Layer5
…
x
Layer4
x
x
R
…
R
R
Layer3
…
Layer2
…
Layer1
x
x
1
2
Fig. 8.9.
Structure of self-constructing neural fuzzy inference network (SONFIN).
The structure of the SONFIN is shown in Fig. 8.9. The five-layered network
realizes a fuzzy model of the following form
Rule
i
: IF
x
1
is
A
i1
and … and
x
n
is
A
in
THEN
y
is
m
oi
+
a
ji
x
j
+ … ,
where
A
ij
is a fuzzy set,
m
oi
is the center of a symmetric membership function on
y
,
and
a
ji
is a consequent parameter. Unlike the traditional TSK model where all the
input variables are used in the output linear equation, only the significant ones are
used in the SONFIN; i.e., some
a
ij
's in the fuzzy rules are zero. We next describe
the functions of the nodes in each of the five layers of the SONFIN.
Layer
1: No computation is done in this layer. Each node in this layer, which
corresponds to one input variable, only transmits input values to the next layer di-
rectly. That is,
()
1
()
1
au x
.
(8.9)
i
i
Layer
2: Each node in this layer corresponds to one linguistic label (small,
large, etc.) of one of the input variables in Layer 1. In other words, the member-
ship value that specifies the degree to which an input value belongs to a fuzzy set
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