Swarm Intelligence

networks—and almost all feedforward networks—do have continuous-

valued nodes, and the states of those nodes, usually in the range between

zero and one, can be interpreted to indicate either probability or fuzzy

truth values.

We should also mention that there are formulas for squashing the in-

puts into the tolerable range, usually zero to one, to make this business

more manageable. The most common formula is referred to as the sig-

moid function, since its output is S-shaped. Its equation is

sx

x

()

exp( )

=

+−

1

1

and its graph is seen in Figure 2.5. When x = 0, s(x) = 0.5. Negative in-

puts result in a value that approaches zero as the x becomes more nega ...