Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 70

Let

 L = the set of all liquids

 P = the set of all potable liquids

Suppose that you have been in the desert for a week with nothing to drink, and you find two bottles (Figure 1.4).

Figure 1.4 Bottles of liquids – front side.

Which bottle do you choose?

Bottle A could contain wash water. Bottle A could not contain sulfuric acid.

A membership value of 0.9 means that the contents of A are very similar to perfectly potable liquids, namely, water.

A probability of 0.9 means that over many experiments that 90% yield B to be perfectly safe and that 10% yield B to be potentially deadly. There is 1 chance in 10 that B contains a deadly liquid.

Observation:

What does the information on the back of the bottles reveal?

After examination, the membership value for A remains unchanged, whereas the probability value for B containing a potable liquid drops from 0.9 to 0.0 (Figure 1.5).

Figure 1.5 Bottles of liquids – back side.

As the previous example illustrates, fuzzy memberships represent similarities to objects that are imprecisely defined, while probabilities convey information about relative frequencies.