A First Course in FUZZY and NEURAL CONTROL

3.10. LEVEL CURVES AND ALPHA-CUTS 123

0

y0.5

(^2468101214) y
z 0 (1.25) = 6

3.9.5 Middleofmaximamethod..................

Middle of maxima, or mean of maxima, takes the average of the smallest and
largest values in the domain on which the fuzzy set assumes its maximum. The
output set obtained in Example 3.6 produces the valuez 0 (1.25) =6+9 2 =7. 5.

0

0.2

0.4

0.6

0.8

y

(^2468101214) y
z 0 (1.25) = 7. 5
This method appears weak, however, for a fuzzy set with two separate plateaus
at the maximum height.
0
0.1
0.2
0.3
0.4
2468
z 0 (1.25) = 4. 5

3.10Levelcurvesandalpha-cuts.....................

Alevel set(orlevel curve)ofafunctionA:X→Ris the setA−^1 (α)of
points mapped byAto a constantα, or in other words, a set of the form

A−^1 (α)={x∈X:A(x)=α} (3.9)