文档介绍：Intelligent Signal Processing part 2
Léonard Studer
IPHE-UNIL
11/10/2017
1
Which for What ?
EC
FL
ANN
Learning Capability
Optimizing Capability
Representing Capability
bi is possible and used:
Goal is to realize processing systems with greater intelligence
11/10/2017
2
Léonard Studer, IPHE-UNIL
Imperfect knowledge
Beliefs
Uncertainties
plete
General rules
Imprecision
Vague
Solutions to these difficulties ?
11/10/2017
3
Léonard Studer, IPHE-UNIL
Fuzzy Logic, Fuzzy Sets or Fuzzy Systems, really ?
Lotfi Zadeh, « Fuzzy Sets » in Info & Control, Vol 8 (1965) pp 29-44
104-105 articles &
102-103 industrial products later…
L. Zadeh, « Fuzzy Logic = Computing with Words » in IEEE Trans on Fuzzy Systems, Vol 4, n° 2 (1996), pp 103-111
11/10/2017
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Léonard Studer, IPHE-UNIL
Fuzzy Sets
“At temperature T, the air is warm”
A fuzzy set is defined by its characteristic function applied to variable T
Characteristic fct of warm fuzzy set
100%
0%
T
25°C
30°C
35°C
Membership µ
11/10/2017
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Léonard Studer, IPHE-UNIL
An element can be in more than one fuzzy set
warm
T
25°C
30°C
35°C
100%
0%
Membership µ
20°C
15°C
10°C
80% pleasant
40% warm
pleasant
More than 100 % is OK with Fuzzy Sets
11/10/2017
6
Léonard Studer, IPHE-UNIL
mon Fuzzy Sets
Triangle Trapeze
…and sigmoid, Gaussian, etc…
But the very shape is not so important, just be sensible !
100%
0%
A
B
C
A
B
C
D
100%
Triangles are handy but gaussians are smoother…
11/10/2017
7
Léonard Studer, IPHE-UNIL
Air temperature example
Let’s define 3 fuzzy sets:
“cold”, “pleasant”, “warm”
T
25°C
30°C
35°C
100%
0%
Membership µ
20°C
15°C
10°C
0°C
5°C
Handy method to catch knowledge expressed in words
11/10/2017
8
Léonard Studer, IPHE-UNIL
Comparison between classical and fuzzy sets
Classical sets
Membership limited to 0% & 100%
No intermediate value
An element is 100% in a set or 100% in plementary
Fuzzy sets
Continuous memberships between 0% an