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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