Digital Signal Processing Reference
In-Depth Information
(a)
1
0.9
0.8
0.7
0.6
min[
μ
(
x
)
μ
(
x
)]
A
A
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
100
X
(b)
1
0.9
0.8
0.7
0.6
0.5
0.4
max[
μ
(
x
)
μ
(
x
)]
A
A
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
100
X
Results of a union b intersection of the fuzzy set A from Fig.
11.2
and its complement A
Fig. 11.4
magnitude value, while the degree of fuzziness reflects the degree of confidence to
the dynamic measurement results at given time instant. The width of MF is directly
related to the rate of change of the criterion signal, which is also a function of applied
digital filters and specific measurement algorithms, and in a way encodes the degree
of conformity between accurate (but not exactly known) and measured criterion
signal values. The amount of information IN in the signal is inversely proportional to
the degree of fuzziness, expressed by the area P under the MF l, and is the highest at
the steady state of measurement (points A, E), but the lowest during transient, when
the signal magnitude changes dynamically (points B, C and D). Utilization of the
fuzzy criteria signals instead of their real counterparts allows for mathematical
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