04 fuzzy ruledecompositions
TRANSCRIPT
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Fuzzy Rule Decomposition
Prof. Dr. Sardi SarDr. Ir. Wahidin Wahab M.Sc.
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Overview
Penggunaan Fuzzy sets sebagai kalkulusuntuk menginterpretasikan natural languagePenggunaan natural language dalambentuk pengetahuan yang dikenal denganrule-based systemDekomposisi dari compound rules menjadibentuk kanonikal sebagai proporsi logikaInterpretasi grafis dari inferensi
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Natural Language
Penggunaan fuzzy sets sebagai dasarmatematis dari natural languageFuzzy sets akan digunakan dalamdeskripsi numerik dan ekspresi yang dapat dimengertiFuzzy set A merepresentasikan fuzziness pada mapping dari atomic term daninterpretasinya, dan dapat dinotasikansebagai membership function
μM(α,y)=μA(y)
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Natural Language (cont’d)
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Natural Language (cont’d)
Basic Operations :α or β = max (μα(y), μβ(y))α and β = min (μα(y), μβ(y))Not α = 1 - μα(y)
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Linguistic Hedges
∫=Y y
y 2)]([ αμαMembership Functions :
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Linguistic Hedges (cont’d)
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Linguistic Hedges (cont’d)
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Rule Based System
Dalam kecerdasan artifisial, ada berbagaicara untuk merepresentasikan ilmupengetahuan
IF premise (antecedent), THEN conclusion (consequent)
Jika kita mengetahui suatu fakta, makadapat ditarik kesimpulan
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Canonical Rule Forms
Assignment statementX=largeSeason = winter
Conditional statementIF x is very hot THEN stopIF the tomato is red THEN the tomato is ripe
Unconditional StatementGo to 9Divide by x
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Decomposition of Compound Rules
Pernyataan yang diucapkan manusia bisaberupa aturan campuran yang berstrukturmisalnya:
IF the room temperature is hot,THEN
IF the heat is onTHEN turn the heat lowerELSEIF (the window is closed) AND (the AC is off)
THEN (turn off the AC)
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Decomposition of Compound Rules (cont’d)
Multiple conjunctive antecedentsIF x is A1 and A2 and . . . and AL THEN y is Bs
IF x is AS THEN BS
Multiple disjunctive antecedentsIF x is A1 or A2 or . . . or AL THEN y is Bs
IF x is As THEN y is Bs
)](),...,(),(min[)( 21 xxxx Ls AAAA μμμμ =
L21S A...AAA III=
LS AAAA UUU ...21=)](),...,(),(max[)( 21 xxxx Ls AAAA μμμμ =
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Decomposition of Compound Rules (cont’d)
Conditional statements with ELSE and UNLESS
IF A1 THEN (B1 ELSE B2)Dapat diartikan sbg :
IF A1 THEN B1
IF not A1 THEN B2
IF A1 (THEN B1) UNLESS A2
Dapat diartikan sbg :IF A1 THEN B1
IF A2 THEN not B1
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Decomposition of Compound Rules (cont’d)
Nested IF-THEN rulesIF A1 THEN (IF A2 THEN (B1))
Dapat dibuat menjadi:IF A1 AND A2 THEN B1
CONTOH LAIN :IF A1 THEN (B1 ELSE IF A2 THEN (B2))
Dapat dibuat menjadi:IF A1 THEN B1
IF not A1 AND A2 THEN B2
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Likelihood and Truth Qualification
“highly” = “minus very very”=(very very)0.75
“unlikely” = “not likely” = 1-”likely”“highly unlikely” = “minus very very unlikely”
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Likelihood and Truth Qualification (cont’d)
Jika suatu variabel fuzzy x memiliki nilai keanggotaaansama dengan 0,85 pada suatu himpunan fuzzy A (μA(x) = 0,85 seperti yang ditunjukkan oleh gambar 8.6, makanilai keanggotaan untuk pernyataan berikut ditunjukkan/ditentukan seperti pada gambar 8.5
Gambar 8.6 titik x memiliki nilai keanggotaan0,85 ketika pernyataannya “true”
x
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Likelihood and Truth Qualification (cont’d)
τ: x is A is “true” μA(Xτ)=0,85τ: x is A is “false” μA(Xτ)=0,15τ: x is A is “fairly true” μA(Xτ)=0,96τ: x is A is “very false” μA(Xτ)=0,04
Gambar 8.5
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Aggregation of Fuzzy Rules
Conjunctive system of rules: output y didapat dari fuzzy intersection dari semuaindividual rule. Memenuhi syarat “AND”
Disjunctive system of rules: output y didapat dari fuzzy union dari semuaindividual rule. Memenuhi syarat “OR”
ryyyy UUU ...21=
ryyyy III ...21=
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Graphical Techniques of Inferences
Case 1: max-min inference method with crisp inputs
Case 2: max product with crisp inputs
rkByAxandAx kkkk ...,,2,1forisTHENisisIF 2211 =
))]](input()),(input([min[max)(21
jiy kkk AABμμμ =
))](input())(input([max)(21
jiy kkk AABμμμ ⋅=
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Cont’d
Case 3: max-min implication with fuzzy inputs
Case 4: correlation product using fuzzy inputs
Dimana k = 1, 2, 3, …, r
)]}]()(max[)],()([min{max[max)( 2121
xxxxy kkk AABμμμμμ ∧∧=
)]]()(max[)]()([max[max)( 2121
xxxxy kkk AABμμμμμ ∧⋅∧=
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Max-Min Inference with Crisp Inputs
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Max-Product Implication with Crisp Inputs
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Max-Min Inference with Fuzzy Inputs
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Correlation-Product (max-product) Inference Using Fuzzy Inputs
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Example
Pada sistem mekanik, energi dari tubuh yang bergerakdisebut sebagai energi kinetik. Jika suatu benda denganmassa m (kilogram) bergerak dengan kecepatan v (m/s), dengan energi kinetik k (joule) adalah k=1/2 mv2. jika kitamemodelkan massa dan kecepatan sebagai input sistemdan energi sebagai output lalu kita amati sistem maka kitadapat mengambil deduksi dua aturan disjunctive sebagaiberikut :Rule 1 :
Rule 2 :
( ) ( ),velocityhighismasssmallisIF 122
111 AxandAx
( )energymediumisTHEN 1By
( ) ( ),velocitymediumismasslargeisIF 222
211 AxorAx
( )energyhighisTHEN 2By
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Case 1
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Case 2
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Case 3
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Case 4