Artificial Neural Networks ECE.09.454/ECE.09.560 Fall 2006

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Artificial Neural Networks ECE.09.454/ECE.09.560
Fall 2006
Lecture 8November 6, 2006

• Shreekanth Mandayam
• ECE Department
• Rowan University
• http//engineering.rowan.edu/shreek/fall06/ann/

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Plan

• Fuzzy Logic and Application to Neural Nets
• Fuzzy Set Theory
• Fuzzy I/O Map
• Fuzzy Inference System
• Fuzzy Neural Nets
• Fuzzy-MLP
• Fuzzy-RBF
• Functional equivalence with RBF
• Final Project Discussion
• Lab Activity

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Fuzzy Logic

• Fuzzy logic or fuzzy set theory is a formal
  system for representing and reasoning with
  imprecise information
• Pioneers
• Lotfi Zadeh http//www.cs.berkeley.edu/People/Facu
  lty/Homepages/zadeh.html
• Bart Kosko http//sipi.usc.edu/kosko/

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Fuzzy Sets Membership Functions
Triangular
Gaussian
1
1
m(x)
m(x)
0
0
x
x
Crisp (Not Fuzzy)
1
m(x)
0
x
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Fuzzy Inference System
Fuzzy Rule Base Rule i IF x1 is Ai1 AND x2 is
Ai2 xm is Aim THEN y1 is Bi1 AND y2 is
Bi2 yn is Bin
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Application Example
Fuzzy Controller for an Air-Conditioner Inputs
Outputs (Temperature Settings) (Fan
Motor Speed) Cold Stop Cool Slow Right
Medium Warm Fast Hot Blast Rules IF Cool
THEN Slow Right Medium Warm Fast
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Fuzzy I/O Map
Function x ? y
blast
IF warm THEN fast
fast
IF right THEN medium
medium
Output (y) Motor Speed
IF cool THEN slow
slow
stop
right
warm
cold
cool
hot
Input (x) Air Temp.
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Fuzzy I/O Map (contd.)
IF x
THEN y
centroid
summed sets
68 degrees 20 cool 70 right
Motor speed 20 slow 70 medium
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Functional Equivalence between Fuzzy Systems and
RBF
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Lab 3 RBF Neural Nets

• http//engineering.rowan.edu/shreek/fall06/ann/la
  b3.html

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Summary