Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 222

operations, such as triangular-norm, a triangular-co-norm, etc ., to combine the
incoming signals to the neuron, the extended networks give rise to a hybrid neural
network based on fuzzy arithmetic operations. The fuzzy neural network
architecture is practically based on such a processing element known as fuzzy
neuron (Fuller,1995).

6.2.1.1 AND Fuzzy Neuron

Consider a perceptron-like structure as shown in Figure 6.4 with n input neurons
acting as fan out elements ( i.e . having the same output values as their inputs) and
with one output neuron. The outputs x i of the input-layer neurons are multiplied by
the connecting weights w i and, thereafter, fed to the output-layer neuron. If,
however, the input signals x i and the weights w i are combined by an S-norm , i.e .
the triangular-conorm

p S , , i " , , , . n (6.1)

wx

i i

i

AND-output
neuron

x 1 w 1

:
:

y

x n

w n

y = T ( S ( W 1 ,X 1 ), …, S ( W n ,X n ))

Figure 6.4. AND fuzzy neuron

and the input information p i is further aggregated by a T-norm , i.e . triangular
norm , to yield the final output of the neuron as

yAND p , p , ! , p T p , p , ! , p

12 n 12 n

(6.2)

TS , , S , , ! , S , .

wx w x w x 11 2 2 nn

then the configuration in Figure 6.4 will represent the implementation of an AND
fuzzy neuron under the condition that the T - norm represents a min operator and
the S-norm represents a max operator . Then the min-max composition

^ `

y min max , , ! , max , . (6.3)

wx w x

11 nn

can be realized by the AND fuzzy neuron.