A First Course in FUZZY and NEURAL CONTROL

236 CHAPTER 7. FUZZY-NEURAL AND NEURAL-FUZZY CONTROL

of the neuron. IfT=minandS=max,then the AND neuron realizes the
max-min compositiony=min{w 1 ∨x 1 ,w 2 ∨x 2 }.

Figure 7.3. AND fuzzy neuron

Example 7.3 (OR)Figure 7.4 illustrates an OR fuzzy neuron. The signalxi
and weightwiare combined by a triangular normTto produce

pi=T(wi,xi),i=1, 2

The input informationpiis aggregated by a triangular conormSto produce
the output

y=OR(p 1 ,p 2 )=S(p 1 ,p 2 )=S(T(w 1 ,x 1 ),T(w 2 ,x 2 ))

of the neuron. IfT =minandS=max, then the OR neuron realizes the

Figure 7.4. OR fuzzy neuron

max-min compositiony=max{w 1 ∧x 1 ,w 2 ∧x 2 }.

7.3 Basic principles of neural-fuzzy systems

In order to process fuzzy rules by neural networks, it is necessary to modify
the standard neural network structure appropriately. Since fuzzy systems are
universal approximators, it is expectedthat their equivalent neural network
representations will possess the same property. As stated earlier, the reason to