Transcript NeuroFuzzy Technologies Workshop

Introduction to
NeuroFuzzy Technologies
Tutorial and Workshop
© Constantin von Altrock
Combining Neural Networks
and Fuzzy Logic
Inform Software Corporation
2001 Midwest Rd.
Oak Brook, IL 60521, U.S.A.

Neural Net Basics

Training Neural Nets

Combining Neural and Fuzzy

Training Fuzzy Logic Systems

Convergence of Technologies

Examples
German Version Available!
Phone 630-268-7550
Fax 630-268-7554
Email: [email protected]
Internet: www.fuzzytech.com
© INFORM 1990-1998
Slide 1
Neural Net Basics:
- Neuron Model  Multiple Inputs, One Output
Axon
 The Output Signal is the Activation
Level of the Neuron
 The Inputs Stem From Outputs of
Other Neurons
: Exciting Synapses
: Inhibiting Synapses
 Inputs Wired to the Neuron Using
Exciting Synapses Increase Activation
Level
 Inputs Wired to the Neuron Using
Inhibiting Synapses Decrease
Activation Level
WARNING: This Neuron Model is a Strong Simplification of “Mother Nature”
© INFORM 1990-1998
Slide 2
Neural Net Basics:
- Mathematical Model X1
Inputs
w1
X2
X3
w2
Output
w3
Y
w4
wn
X4
...
Xn
Propagation Function
Activation Function
Y
n
w i . x i + O-
f=
i=0
© INFORM 1990-1998
f
Slide 3
Neural Net Basics:
- Multilayer Nets Input Signal
Input Layer
© INFORM 1990-1998
Output Signal
1. Hidden Layer
2. Hidden Layer
Output Layer
Slide 4
Training Neural Nets:
- Pavlovs’ Dogs Before Learning
Food
Bell
Food
After Learning
Bell
Food
Bell
Food
Bell
Training Increases
the Weight of this Synapse
Dog Salivates
Dog Salivates
Dog Salivates
Dog Salivates
Hebb’s Learning Rule:
Increase weight to active input neuron, if the output of this
neuron should be active,decrease weight to active input
neuron, if the output of this neuron should be inactive.
© INFORM 1990-1998
Slide 5
Combining
Neural and Fuzzy
 Neural Networks have their Strengths
 Fuzzy Logic has its Strengths
Neural Nets
Fuzzy Logic
Knowledge
Representation
Implicit, the system
cannot be easy
interpreted or modified (-)
Explicit, verification and
optimization easy and
efficient (+++)
Trainability
Trains itself by learning
from data sets (+++)
None, you have to define
everything explicitly (-)
Get “best of both worlds”:
Explicit Knowledge Representation from Fuzzy Logic
with Training Algorithms from Neural Nets
© INFORM 1990-1998
Slide 6
Training
Fuzzy Logic Systems
Fuzzification
Defuzzification
Inference
 Many Different Ways Exist to Train a Fuzzy
Logic System
 NeuroFuzzy := Use Error Backpropagation
 Emulate Fuzzy Logic System as Neural Net
 Each Component of a Fuzzy Logic System
is Represented as Part of a Neural Net
 Apply EPG to this ‘Neural Net’
 : EPG Requires Differentiability
 : Use Gradient Estimators
 : Use Fuzzy Associative Memories
© INFORM 1990-1998
Slide 7
Convergence of
Technologies
Year: Computing:
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
Neural Networks:
Fuzzy Logic:
Relay/Valve Based
Transistors
Neuron Model (McCulloch/Pitts)
Training Rules (Hepp)
Small Scale Integration Delta Rule (Wirow/Hoff)
Seminal Paper (Zadeh)
Large Scale Integration Multilayer Perceptron, XOR
Artificial Intelligence
Fuzzy Control (Mamdani)
Hopfield Model (Hopfield/Tank)
Backpropagation (Rumelhart) Broad Application in Japan
Bidir. Assoc. Mem. (Kosko) Broad Application in Europe
Broad Application in the U.S.
Soft Computing, NeuroFuzzy
© INFORM 1990-1998
Slide 8