Chap 12: ANFIS and Other Models

1
Chap 12 ANFIS and Other Models
Neura-Fuzzy Systems
2
Neuro-Fuzzy and Soft Computing
Soft Computing
3
Fuzzy Modeling
Unknown target system
y
Fuzzy Inference system
y

• Given desired i/o pairs (training data set) of
  the form
• (x1, ..., xn y), construct a FIS to match the
  i/o pairs

• Two steps in fuzzy modeling
• structure identification --- input selection,
  MF numbers
• parameter identification --- optimal parameters

4
Neuro-Fuzzy Modeling

• Basic approach of ANFIS

Adaptive networks
Generalization
Specialization
Neural networks
Fuzzy inference systems
ANFIS
5
ANFIS
6
Four-Rule ANFIS
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ANFIS Parameter ID

• Hybrid training method

nonlinear parameters
linear parameters
w1
A1
P
w1z1
x
A2
P
S
Swizi
B1
P
/
z
y
B2
P
w4z4
Swi
w4
S
forward pass
backward pass
fixed
steepest descent
MF param. (nonlinear)
least-squares
fixed
Coef. param. (linear)
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ANFIS Structure ID

• Input selection
• Input space partitioning

To select relevant input for efficient modeling
Grid partitioning
Tree partitioning
Scatter partitioning

• C-means clustering
• mountain method
• hyperplane clustering

• CART method

9
Fuzzy Neural Network (Zhang-Kandel)

• Graphics representation

A1
B1
C1
w1
Z
z3
X
Y
za
zb
A2
B2
C2
w2
zd
zc
Z
zy
zp
X
Y
T-norm
Z1Za, Zb
Z2Zc, Zd
X
Y
x is 4.5
y is 56.8
Z4Zy, Zp
10
Conclusions

• Contributing factors to successful applications
  of neuro-fuzzy and soft computing
• Sensor technologies
• Cheap fast microprocessors
• Modern fast computers