Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 64

Classical sets are considered crisp because their members satisfy precise properties. For example, for illustration, let H be the set of integer real numbers from 6 to 8. Using set notation, one can express H as:

(1.1)

One can also define a function μ_H(r) called a membership function to specify the membership of r in the set H,

(1.2)

The expression states:

 r is a member of the set H (membership in H = 1) if its value is 6, 7, or 8. Otherwise, it is not a member of the set (membership in H = 0).

One can also present the same information graphically as in Figure 1.2.

Whichever representation is chosen, it remains clear that every real number, r, is surrounded by crisp boundaries and is either in the set H or not in the set H.

Moreover, because the membership function μ maps the associated universe of discourse of every classical set onto the set {0, 1}, it should be evident that crisp sets correspond to a two‐valued logic. An element is either in the set or it is not in the set, and it is either TRUE or it is FALSE.

Figure 1.2 Membership in subset H.