Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 69

Consider the phrase:

 Etienne is old.

The phrase could also be expressed as:

 Etienne is a member of the set of old people.

If Etienne is 75, one could assign a fuzzy truth value of 0.8 to the statement. As a fuzzy set, this would be expressed as:

 μold (Etienne) = 0.8

From what we have seen so far, membership in a fuzzy subset appears to be very much like probability. Both the degree of membership in a fuzzy subset and a probability value have the same numeric range: 0–1. Both have similar values: 0.0 indicating (complete) nonmembership for a fuzzy subset and FALSE for a probability and 1.0 indicating (complete) membership in a fuzzy subset and TRUE for a probability. What, then, is the distinction?

Consider a natural language interpretation of the results of the previous example. If a probabilistic interpretation is taken, the value 0.8 suggests that there is an 80% chance that Etienne is old. Such an interpretation supposes that Etienne is or is not old and that we have an 80% chance of knowing it. On the other hand, if a fuzzy interpretation is taken, the value of 0.8 suggests that Etienne is more or less old (or some other term corresponding to 0.8).

To further emphasize the difference between probability and fuzzy logic, let's look at the following example.