A First Course in FUZZY and NEURAL CONTROL

7.1. FUZZY CONCEPTS IN NEURAL NETWORKS 231

Figure 7.1. Neural network with fuzzy neurons

approximate functions from numerical input-output data(xi,yi),i=1, 2 ,...,n.
Fuzzy-neural networks are a more general computational structure with which
function approximation can be extended to linguistic data.
Consider a set of fuzzy rules of the form

Ri:IfxisAithenyisBi (7.1)

i=1,...,n,whereAiandBiare products of fuzzy sets

Ai(x)=





YN

j=1

Aij



(x)=

^N

j=1

Aij(xj)

Bi(y)=

√M

Y

k=1

Bik

!

(y)=

^M

k=1

Bki(yk)

Each rule in (7.1) can be interpreted as a training pattern for a multi-layer
neural network, where the antecedent part of the rule is the input to the neural
network, and the consequent part of the rule is the desired output of the neural
net. Equation (7.1) therefore would constitute a

ïsingle-input, single-output (SISO) system ifN=M=1.

ïmulti-input, single-output (MISO) system ifN> 1 ,M=1.

ïmulti-input, multi-output (MIMO) system ifN> 1 ,M> 1.