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NOT Clever can be written mathematically as:
(10.8)
Hedges
Hedges are unary operators that can be employed to modify the meaning of
a fuzzy set. Two commonly used hedges are VERY and FAIRLY. For a
fuzzy set A, VERY modifies it like so:
(10.9)
In other words, it results in the square of the membership degree. FAIRLY
modifies a fuzzy set by taking the square root of the membership degree,
like so:
(10.10)
The effect of these hedges is best seen graphically. Figure 10.9 shows how
VERY narrows the membership function and how FAIRLY widens it. This
is intuitive because the criteria for membership in a set modified by
FAIRLY should be more relaxed than for the set itself. And the opposite
holds for VERY — the criterion is tightened.
Fuzzy Linguistic Variables
A fuzzy linguistic variable (or FLV) is the composition of one or more
fuzzy sets to represent a concept or domain qualitatively. Given our earlier
example, the sets Dumb, Average, and Clever are members of the fuzzy lin
-
guistic variable IQ. This can be written in set notation as:
IQ ={Dumb, Average, Clever}
Fuzzy Logic | 423
Fuzzy Linguistic Variables
Figure 10.9. Modifying the shape of a membership function using fuzzy hedges
()' 1 ()
Clever Clever
Fx Fx=-
2
()
(())
VERY A A
FFx=
()
()
FAIRLY A A
FFx=

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