ANFIS Adaptive neuro-fuzzy inference system

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ANFISAdaptive neuro-fuzzy inference system
First-order Sugeno fuzzy model (2 inputs and 2
rules) Rule 1 IF x is A1 AND y is
B1 THEN f1p1xq1yr1 Rule 2 IF x is A2 AND y is
B2 THEN f2p2xq2yr2
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ANFIS
Layer 1 Premise parameters
 
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ANFIS
Layer 2 T-norm operator
 
T-norm operator that perform fuzzy AND For
j1,2, ..n (n of inputs)
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ANFIS
Layer 3 Outputs of the layer 3 are normalised
firing strengths
 
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ANFIS
Layer 4 Consequent parameters
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ANFIS
Layer 5 Crisp output
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Example ANFIS
Rule 1 IF x is small (A1) AND y is small (B1)
THEN f1small Rule 2 IF x is large (A2) AND y is
large (B2) THEN f2large
A1
B1
B2
A2
For x3 and y4, find the crisp output of the
Sugeno fuzzy system
Result is ?
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ANFIS
Two passes in the hybrid learning procedure
Forward Pass Backward Pass
Premise Parameters (nonlinear) Fixed Gradient descent
Consequent parameters (linear) Least-square estimator Fixed
Signals Node outputs Error signals
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Example(Jang et al., Neuro-Fuzzy and Soft
Computing, Prentice Hall, 1997)ANFIS is used to
model a two-dimensional sinc equation defined by
x and y are in the range -10,10 Number of
membership functions for each input 4 Number of
rules 16
10
x
y
Initial membership functions
Final (trained) membership functions after 100
epochs
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• Fuzzy Logic Applications
• Digital Fuzzy Processor
• Omron was the first to launch a controller
  employing fuzzy logic for improved control and
  tuning
• Production of the world's fastest digital fuzzy
  processor (DFP) in 1990.
• With a reasoning speed of 10 MFLIPS (1 million
  fuzzy logic inferences per second)

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• Applications of Fuzzy Logic to Traffic Signal
  Control
• (Budi Yulianto, Application of fuzzy logic to
  traffic signal control under mixed traffic
  conditions, tec, October 2003, pp332-335)

Input Variables for Fuzzy Logic Traffic Signal
Controller Maximum Queue Length (in metres) the
distance in metres from the stop-line over which
vehicles have queued Average Occupancy Rate ()
percentage of time that the detection area was
occupied by one or more vehicles. Output Variable
for the Controller Weight 0, 100 the degree
of green traffic signal requirement
Improvement (up to) 25 in average travel time
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of rules 16
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Rule Table/Matrix
Maximum Queue Length
L M H VH
L VVL L M H
M VL L H VH
H L M H VVH
VH M H VH VVH
Average Occupancy Rate
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• More fuzzy logic applications http//www.aptronix.
  com/fuzzynet/index.htm

More fuzzy logic applications use fuzdemos in
MATLAB
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• Next week
• LAB ANFIS
• (Next week Tuesday only
• LAB will start at 6pm- before the lecture)
• Lecture KBS (Dr. Innocent)
• (Week 11-Revision for Fuzzy Logic)