1 Pertemuan 21 MEMBERSHIP FUNCTION Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1.
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Transcript of 1 Pertemuan 21 MEMBERSHIP FUNCTION Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1.
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Menjelaskan konsep fungsi keanggotaan pada logika fuzzy.
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FUZZY LOGICFUZZY LOGIC
• Lotfi A. Zadeh“Fuzzy Sets”, Information and Control, Vol 8, pp.338-353,1965.
Clearly, the “class of all real numbers which are much greater than 1,” or “the class of beautiful women,” or “the class of tall men,” do not constitute classes or sets in the usual mathematical sense of these terms (Zadeh, 1965).
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PROF. ZADEHPROF. ZADEH
Fuzzy theory should not be regarded
as a single theory, but rather a
methodology to generalize a specific
theory from being discrete, to being
more continuous
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WHAT IS FUZZY LOGICWHAT IS FUZZY LOGIC
Fuzzy logic is a superset of conventional (boolean) logic
An approach to uncertainty that combines real values [0,1] and logic operations
In fuzzy logic, it is possible to have partial truth values
Fuzzy logic is based on the ideas of fuzzy set theory and fuzzy set membership often found in language
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WHY USE FUZZY LOGIC ?WHY USE FUZZY LOGIC ?
An Alternative Design Methodology Which Is Simpler, And Faster • Fuzzy Logic reduces the design
development cycle • Fuzzy Logic simplifies design complexity • Fuzzy Logic improves time to market
A Better Alternative Solution To Non-Linear
Control • Fuzzy Logic improves control performance • Fuzzy Logic simplifies implementation • Fuzzy Logic reduces hardware costs
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WHEN USE FUZZY LOGIC WHEN USE FUZZY LOGIC
Where few numerical data exist and where only ambiguous or imprecise information maybe available.
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FUZZY SETFUZZY SET
In natural language, we commonly employ: classes of old people Expensive cars numbers much greater than 1
Unlike sharp boundary in crisp set, here boundaries seem vague
Transition from member to nonmember appears gradual rather than abrupt
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FUZZY SET AND MEMBERSHIP FUZZY SET AND MEMBERSHIP FUNCTIONFUNCTION
Universal Set X – always a crisp set. Crisp set assigns value {0,1} to
members in X Fuzzy set assigns value [0,1] to
members in X These values are called the
membership functions . Membership function of a fuzzy set A is
denoted by : A: X [0,1]A: [x1/1, x2/…, xn/n}
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HIMPUNAN HIMPUNAN CRISP DAN FUZZYCRISP DAN FUZZY
Himpunan kota yang dekat dengan Bogor
• A = { Jakarta, Sukabumi, Cibinong, Depok }
CRISP
• B = { (0.7 /Jakarta) , (0.6 /Sukabumi) , (0.9
/Cibinong) , (0.8/Depok) } FUZZY
Angka 0.6 – 0.9 menunjukkan tingkat
keanggotaan ( degree of membership )
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TINGGI BADANTINGGI BADAN
0
1
0
1
150 160155
150 160155
0,5
tinggi
tinggi
sedang
sedang
CRISP
FUZZY
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AGEAGE
0 20 40 60 80 100
0
0.5
1
Age
Mem
ber
ship old
more or less old
youngvery young
not very young
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MEMBERSHIP FUNCTIONMEMBERSHIP FUNCTION
0
0.5
1
(a) (d) (g) (j)
0
0.5
1
(b) (e) (h) (k)
-100 0 1000
0.5
1
(c)-100 0 100
(f)-100 0 100
(i)-100 0 100
(l)
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LINGUISTIC VARIABLESLINGUISTIC VARIABLES
Linguistic variable is ”a variable whose
values are words or sentences in a natural
or artificial language”. Each linguistic
variable may be assigned one or more
linguistic values, which are in turn connected
to a numeric value through the mechanism
of membership functions.
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LINGUISTIC VARIABLESLINGUISTIC VARIABLES
Fuzzy linguistic terms often consist of two parts:
1) Fuzzy predicate : expensive, old, rare, dangerous, good, etc.
2) Fuzzy modifier: very, likely, almost impossible, extremely unlikely, etc.
The modifier is used to change the meaning of predicate and it can be grouped into the following two classes:
a) Fuzzy truth qualifier or fuzzy truth value: quite true, very true, more or less true, mostly false, etc.
b) Fuzzy quantifier: many, few, almost, all, usually, etc.
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FUZZY PREDICATEFUZZY PREDICATE
Fuzzy predicate
– If the set defining the predicates of individual is a fuzzy set, the predicate is called a fuzzy predicate
Example
– “z is expensive.”
– “w is young.”
– The terms “expensive” and “young” are fuzzy terms.
Therefore the sets “expensive(z)” and “young(w)” are fuzzy sets
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FUZZY PREDICATEFUZZY PREDICATE
When a fuzzy predicate “x is P” is given, we can interpret it in two ways :
• P(x) is a fuzzy set. The membership degree of x in the set P is defined by the membership function P(x)
• P(x) is the satisfactory degree of x for the property P.
Therefore, the truth value of the fuzzy predicate is defined by the membership function :
Truth value = P(x)
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FUZZY VARIABLESFUZZY VARIABLES
Variables whose states are defined by linguistic concepts like low, medium, high.
These linguistic concepts are fuzzy sets themselves.
Low HighVeryhigh
TemperatureMem
ber
ship
Trapezoidal membership functions
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FUZZY VARIABLESFUZZY VARIABLES
Usefulness of fuzzy sets depends on our capability to construct appropriate membership functions for various given concepts in various contexts.
Constructing meaningful membership functions is a difficult problem –GAs have been employed for this purpose.
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EXAMPLEEXAMPLE
if speed is interpreted as a linguistic variable, then its term set T (speed) could be T = { slow, moderate, fast, very slow, more or less fast, sligthly slow, ……..}.
where each term in T (speed) is characterized by a fuzzy set in a universe of discourse U = [0; 100]. We might interpret
• slow as “ a speed below about 40 km/h"
• moderate as “ a speed close to 55 km/h"
• fast as “ a speed above about 70 km/h"
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NORMALIZED NORMALIZED DOMAIN INPUTDOMAIN INPUT
• NB (Negative Big), NM (Negative Medium)
• NS (Negative Small), ZE (Zero)
• PS (Positive Small), PM (Positive Medium)
• PB (Positive Big)
A possible fuzzy partition of [-1; 1].