Matakuliah
Tahun
Versi
: H0383/Sistem Berbasis Pengetahuan
: 2005
: 1/0
Pertemuan 7
Ketidakpastian dalam Rules
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Memilih suatu metode untuk mengatasi
ketidakpastian pada rule based systems
2
Outline Materi
• Sebab Ketidakpastian
• Certainty Factor
• Fuzzy Logic
3
Ketidakpastian
Sebab ketidak pastian:
• Informasi partial
• Informasi not fully reliable
• Representation languages is inherently
imprecise
• Info come from multiple sources and conflict.
• Info is approximate.
• Non absolute cause effect relationship exists.
4
Certainty Factor
• Certainty Factor = Measure of Belief Measure of Disbelief
• CF[P,E] = MB[P,E] – MD[P,E]
• P=probability
• E= evidence
5
Certainty Factor
• If inflation is above 5% (CF=50%) and if
unemployment rate is above 7% (CF
70%) and if bond prices decline
(CF=100%) then stock prices decline.
• CF = min CF(A,B,C). Then stock prices
decline( CF = 50%).
• OR- maximum CF(A,B,C)
6
Certainty Factor
R1 If the inflation rate is less than 5% then
stock market price goes up (CF1=0.7)
R2 If unemployment is less than 7% then
stock market price goes up (CF2 = 0.6)
• CF (R1,R2) = CF1 + CF2[1-CF1] = 0.88
7
Fuzzy Logic
• Generalisasi logika (tidak hanya 1/0)
• Aplikasi penting: Sistem Pengaturan
• Keuntungan:
– Pengaturan Lebih “smooth” dari sekedar
ON/OFF
– Tidak memerlukan model matematika
• Kekurangan:
– Stabilitas sistem tidak terdefinisi secara
eksakta.
8
Fuzzy Logic
Membership function dari
usia
µ(x)
muda
dewasa
tua
1
0
24
40
60
x
µ(x) : membership function
µ(15) = 1/muda + 0/dewasa +0/tua
µ(24) = 0,6/muda + 0,4/dewasa +0/tua
µ(40) = 0/muda + 1/dewasa +0/tua
9
Fuzzy Logic
Operasi Logika Fuzzy
µA(x) AND µB(y) = minimum(µA(x) , µB(y))
µA(x) OR µB(y) = maximum(µA(x) , µB(y))
NOT µA(x) = 1 - µA(x)
µA(x) = 0.7,
µB(y) = 0.5
µA(x) AND µB(y) = 0.5
µA(x) OR µB(y) = 0.7
NOT µA(x) = 1 – 0.7 = 0.3
10
Fuzzy Logic
µ
1
µ
1µ
0
0
dingin
10
normal
25
Suhu [ºC]
panas
40
kecil
sedang
besar
5
0
10
Arus listrik [ampere]
IF suhu = dingin THEN aruslistrik = kecil
IF suhu = normal THEN aruslistrik = sedang
IF suhu = panas THEN aruslistrik = besar
11
Fuzzy Logic
µ
dingin
normal
panas
1
µ
1µ
kecil
sedang
besar
0,8
0,2
0
0
10
27
Suhu [ºC]
40
0
5
10
Arus listrik [ampere]
12
Fuzzy Logic
• Fuzzy Control
e(t)
U(t)
Regulator
de(t)/dt
13
Fuzzy Logic
• Fuzzy Control
Rule Base
Fuzzy
Reasoning
(Inferensi)
Fuzzification
defuzzification
14
Fuzzy Logic
• Fuzzy Position Control
e
de
u
Fuzzy
variable
-1000
-500
-200
-5
-800
-400
-160
-4
-600
-300
-120
-3
-400
-200
-80
-2
-200
-100
-40
-1
0
0
0
0
200
100
40
1
400
200
80
2
600
300
120
3
800
400
160
4
1000
500
200
5
NB
NK
NOL PK
-5 -4 -3 -2 -1 0 1
2
PB
3 4 5
15
Fuzzy Logic
•
•
•
•
•
•
•
If e is PB & de is any THEN u is PB
If e is PK & de is NOL THEN u is PK
If e is PK & de is PK THEN u is PK
If e is NOL & de is PK THEN u is NOL
If e is NOL & de is NK THEN u is NK
If e is NK & de is NK THEN u is NK
If e is NB & de is any THEN u is NB
16
Fuzzy Logic
• Resoning w. Fuzzy Logic
NB
NK
PB
NOL PK
-5 -4 -3 -2 -1 0
e de
1
2
3
4
5
17
Fuzzy Logic
•
•
•
•
•
•
e= 0.8/NB + 0.2/NK (dari gambar)
de=0.4/NB + 0.6/NK
If e = NB and de = any THEN u=NB
If e = NK and de = NK THEN u=NK
If e = 0.8/NB and de = 0.4/NB THEN u=0.4NB
If e = 0.2/NK and de = 0.6/NK THEN u=0.2/NK
18
Fuzzy Logic
• Defuzzyfication (center of area method)
NB
NK
NOL PK
-5 -4 -3 -2 -1 0 1
2
PB
3 4 5
19
Penutup
• Merepresentasikan bahasa verbal
manusia ke dalam suatu simbol logika
dapat mengakibatkan ketidakpastian.
• Certainty Factor dan Fuzzy Logic dapat
mengatasi ketidakpastian dalam rulebased systems
20