Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

designed the weights (W) of a single-layered feed-forward neural net by taking
the product of input feeder (I) and the transpose of the output feeder (O) :
T
W = I o O , where "o" denotes the max-min composition operator.
∼ ∼
Once the weight matrix between the output and the input layer is formed, one
/
/
can estimate an output vector o when the input vector I is given:
∼
∼
/ /
o Wo I .
∼ =
∼
Analogously, the input vector
by
w o .
/ T /
∼ = I o
∼
/
∼ I can also be estimated, when
/
o is given
Recently, Saha and Konar [22] designed a new methodology for estimation of
inversion of fuzzy matrix, W. By using their definition, one can compute I' by
w o
/ −1 /
I = o , where W
∼
−1 is defined as W −1 o W → I, the '→' symbol
represents 'tends to' and I is the identity matrix. There exist matrices for a
(n × n) W matrix. The best inverse, which is defined as wbest −1 , is where
2
− 1
∑ ∑ δ ij
is minimum for [ δ ij] = [ ( w o best w ) − I]
and
i j
is generally used for estimation of I' using
It may be added that in very special cases
matrix support Kosko's model [14].
14.9 Fuzzy Neural Nets
n
n
∼
/ /
− 1
w
I = o best
∼
− 1 T
w = best w
o
∼
, and thus the inverse
Conventional sets include elements with membership values zero or one.
However, for many real world problems, the membership value of an element
.