1. Introduction to NeuroFuzzy Technologies © INFORM 1990-1998Slide 1 Tutorial and Workshop © Constantin von Altrock Inform Software Corporation 2001 Midwest Rd. Oak Brook, IL 60521, U.S.A. German Version Available! Phone 630-268-7550 Fax 630-268-7554 Email: fuzzy@informusa.com Internet: www.fuzzytech.com Tutorial and Workshop © Constantin von Altrock Inform Software Corporation 2001 Midwest Rd. Oak Brook, IL 60521, U.S.A. German Version Available! Phone 630-268-7550 Fax 630-268-7554 Email: fuzzy@informusa.com Internet: www.fuzzytech.com Combining Neural Networks and Fuzzy Logic X XNeural Net Basics X XTraining Neural Nets X XCombining Neural and Fuzzy X XTraining Fuzzy Logic Systems X XConvergence of Technologies X XExamples Combining Neural Networks and Fuzzy Logic X XNeural Net Basics X XTraining Neural Nets X XCombining Neural and Fuzzy X XTraining Fuzzy Logic Systems X XConvergence of Technologies X XExamples

2. Neural Net Basics: - Neuron Model - Neural Net Basics: - Neuron Model - © INFORM 1990-1998Slide 2 X XMultiple Inputs, One Output X XThe Output Signal is the Activation Level of the Neuron X XThe Inputs Stem From Outputs of Other Neurons X XInputs Wired to the Neuron Using Exciting Synapses Increase Activation Level X XInputs Wired to the Neuron Using Inhibiting Synapses Decrease Activation Level X XMultiple Inputs, One Output X XThe Output Signal is the Activation Level of the Neuron X XThe Inputs Stem From Outputs of Other Neurons X XInputs Wired to the Neuron Using Exciting Synapses Increase Activation Level X XInputs Wired to the Neuron Using Inhibiting Synapses Decrease Activation Level WARNING: This Neuron Model is a Strong Simplification of “Mother Nature”

3. Neural Net Basics: - Mathematical Model - Neural Net Basics: - Mathematical Model - © INFORM 1990-1998Slide 3

4. Neural Net Basics: - Multilayer Nets - Neural Net Basics: - Multilayer Nets - © INFORM 1990-1998Slide 4

5. Training Neural Nets: - Pavlovs’ Dogs - Training Neural Nets: - Pavlovs’ Dogs - © INFORM 1990-1998Slide 5 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.

6. Combining Neural and Fuzzy Combining Neural and Fuzzy © INFORM 1990-1998Slide 6 X XNeural Networks have their Strengths X XFuzzy Logic has its Strengths Neural Nets Knowledge Representation Fuzzy Logic Trainability Implicit, the system cannot be easy interpreted or modified (-) Trains itself by learning from data sets (+++) Explicit, verification and optimization easy and efficient (+++) None, you have to define everything explicitly (-) Get “best of both worlds”: Explicit Knowledge Representation from Fuzzy Logic with Training Algorithms from Neural Nets

7. Training Fuzzy Logic Systems Training Fuzzy Logic Systems © INFORM 1990-1998Slide 7 X XMany Different Ways Exist to Train a Fuzzy Logic System X XNeuroFuzzy := Use Error Backpropagation X XEmulate Fuzzy Logic System as Neural Net X XEach Component of a Fuzzy Logic System is Represented as Part of a Neural Net X XApply EPG to this ‘Neural Net’ X X  : EPG Requires Differentiability X X  : Use Gradient Estimators X X  : Use Fuzzy Associative Memories X XMany Different Ways Exist to Train a Fuzzy Logic System X XNeuroFuzzy := Use Error Backpropagation X XEmulate Fuzzy Logic System as Neural Net X XEach Component of a Fuzzy Logic System is Represented as Part of a Neural Net X XApply EPG to this ‘Neural Net’ X X  : EPG Requires Differentiability X X  : Use Gradient Estimators X X  : Use Fuzzy Associative Memories

8. Convergence of Technologies © INFORM 1990-1998Slide 8 Year: 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Year: 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Computing: Relay/Valve Based Transistors Small Scale Integration Large Scale Integration Artificial Intelligence Computing: Relay/Valve Based Transistors Small Scale Integration Large Scale Integration Artificial Intelligence Neural Networks: Neuron Model (McCulloch/Pitts) Training Rules (Hepp) Delta Rule (Wirow/Hoff) Multilayer Perceptron, XOR Hopfield Model (Hopfield/Tank) Backpropagation (Rumelhart) Bidir. Assoc. Mem. (Kosko) Neural Networks: Neuron Model (McCulloch/Pitts) Training Rules (Hepp) Delta Rule (Wirow/Hoff) Multilayer Perceptron, XOR Hopfield Model (Hopfield/Tank) Backpropagation (Rumelhart) Bidir. Assoc. Mem. (Kosko) Fuzzy Logic: Seminal Paper (Zadeh) Fuzzy Control (Mamdani) Broad Application in Japan Broad Application in Europe Broad Application in the U.S. Fuzzy Logic: Seminal Paper (Zadeh) Fuzzy Control (Mamdani) Broad Application in Japan Broad Application in Europe Broad Application in the U.S. Soft Computing, NeuroFuzzy