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| Preface | |
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| Introduction | |
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| Fuzzy Logic And Engineering | |
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| Preview | |
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| Fuzziness as Vagueness: Everything is a Matter of Degree | |
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| The History of Vague Logic | |
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| Fuzzy Sets and Systems | |
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| Fuzzy Systems in Commercial Products | |
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| Adaptive Fuzzy Systems and the Search for Better Rules | |
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| Overview of Fuzzy Logic, Set Theory, and Systems | |
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| References | |
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| Homework Problems | |
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| Fuzzy Function Approximation | |
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| Additive Fuzzy Systems | |
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| Fuzzy Function Approximation as a Fuzzy Cover | |
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| The Curse of Dimensionality: Rule Explosion and Optimal Rules | |
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| Additive Fuzzy Systems: The Standard Additive Model | |
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| Set Functions in SAMs | |
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| The "Center of Gravity" Method as a Constant-Volume SAM | |
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| Generalized SAMs and the TSK Model: Convex Sums of Nonlinear Systems | |
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| Generalized SAMs as Set Mappings and Correlators: The Set SAM | |
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| Combining Fuzzy Systems: Convex Sums of Expert Responses | |
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| Fuzzy Systems as Conditional Means: The Probability Connection | |
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| Function Approximation with Additive Fuzzy Systems | |
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| Function Representation with SAMs | |
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| Learning in SAMs: Unsupervised Clustering and Supervised Gradient Descent | |
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| Optimal Additive Systems: Patch the Bumps | |
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| Feedback SAMs and Fuzzy Cognitive Maps | |
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| References | |
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| Homework Problems | |
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| Ellipsoidal Fuzzy Systems | |
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| Learning with Ellipsoid Rules | |
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| Additive Fuzzy Systems | |
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| Ellipsoidal Fuzzy Rules | |
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| Unsupervised Covariance Ellipsoid Estimation | |
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| Supervised Learning of Fuzzy Rule Patches | |
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| Hybrid System: Unsupervised and Then Supervised Ellipsoidal Learning | |
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| Optimal Function Approximation | |
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| Conclusions | |
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| References | |
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| Unsupervised Competitive Learning | |
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| Homework Problems | |
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| Software Problems | |
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| Fuzzy Control and Chaos | |
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| Fuzzy Control for Platoons of Smart Cars | |
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| Preview | |
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| Platoons of Smart Cars | |
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| Fuzzy Throttle Controller | |
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| Brake Controller | |
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| FTC Simulation Results | |
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| Hybrid Ellipsoidal Function Learning | |
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| Control Surface Learning | |
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| Gap Control Test | |
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| Conclusions | |
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| References | |
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| Homework Problems | |
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| Fuzzy Chaos and Recursive Partitioning | |
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| Preview | |
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| Fuzzy Systems as Rule Coverings: Approximating Chaos | |
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| Fuzzy System Design | |
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| Approximating Functions | |
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| Approximating Dynamical Systems and Chaos | |
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| Conclusions | |
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| References | |
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| Homework Problems | |
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| Fuzzy Signal Processing | |
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| Fuzzy Filters For Impulsive Noise | |
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| Preview | |
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| Filtering Impulsive Noise | |
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| Alpha-Stable Noise: Covariation Versus Covariance | |
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| Additive Fuzzy Systems | |
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| Fuzzy Prediction with Covariation Rules | |
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| Fuzzy Filters with Covariation Rules | |
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| Conclusion | |
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| References | |
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| Appendix 6.A: Competitive AVQ Algorithm for Local Means and Covariations | |
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| Homework Problems | |
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| Fuzzy Subband Image Coding | |
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| Preview | |
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| Tilings of the Time-Frequency Plane | |
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| Subband Image Coding | |
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| Fuzzy Virtual Tilings for Subband Coding | |
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| Simulation Results | |
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| Conclusion | |
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| References | |
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| Homework Problems | |
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| Fuzzy Communication | |
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| Adaptive Fuzzy Frequency Hopping for Spread Spectrum | |
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| Preview | |
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| Frequency Hopping Spread Spectrum | |
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| Fuzzy Pseudorandom Number Generator | |
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| Functional Description of the Fuzzy System | |
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| Simulation Results | |
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| Comparison with a Shift Register with Linear Feedback | |
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| Conclusion | |
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| References | |
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| Derivation of the Centroid as the Conditional Mean for the Frequency-Hopping SAM | |
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| Homework Problems | |
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| Fuzzy Signal Detection in Impulsive Noise | |
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| Preview | |
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| Fuzzy Signal Detection in Noise | |
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| Source Model | |
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| Scalar Channel Model | |
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| Fuzzy Detector | |
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| Simulation Results | |
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| Conclusion | |
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| References | |
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| Functional and Geometrical View of Fuzzy Sets | |
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| Fuzziness and Clarity Measures | |
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| Homework Problems | |
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| Fuzzy Hardware | |
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| Adaptive VLSI Additive Fuzzy Systems | |
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| Preview: SAMs in Silicon | |
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| VLSI for Fuzzy Systems | |
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| The SAM Architecture and VLSI | |
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| Set SAMs and Second-Order Statistics | |
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| Adaptive Digital SAM | |
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| Adaptive SAM VLSI | |
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| ASAM Chip | |
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| ASAM Operation | |
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| Conclusion | |
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| References | |
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| Homework Problems | |
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| Optical Additive Fuzzy Systems | |
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| Preview: SAMs in Optics | |
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| Fuzzy Computation: Electronics in Time Versus Optics in Space | |
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| Parallel Fuzzy-Set Function Optical Processor | |
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| Scanning Laser Diode Fuzzy System Processor | |
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| DSTOP Fuzzy System Processor | |
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| Optical Fuzzy System Processing: Present and Future | |
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| References | |
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| Homework Problems | |
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| Computing in Fuzzy Cubes | |
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| Fuzzy Cubes and Fuzzy Mutual Entropy | |
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| Preview | |
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| The First Theorem: Addition as Fuzzy Mutual Entropy | |
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| Fuzzy Sets as Points in Hypercubes: Degrees of Subsethood | |
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| Fuzziness and Entropy | |
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| Fuzzy Mutual Entropy | |
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| The Proof: Diffeomaps Between Real Spaces and Fuzzy Cubes | |
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| Information Fields: Shannon Entropy From Fuzzy Mutual Entropy | |
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| The Field Equations of Fuzzy Information: It from Fit | |
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| Conclusions | |
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| References | |
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| Homework Problems | |
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| Adaptive Subsethood for Radial Basis Fuzzy Systems | |
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| Preview | |
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| Adaptive Subsethood in a Radial Basis Standard Additive Model | |
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| The Measure of Mutual Subsethood: Fuzzy Equivalence | |
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| Mutual Subsethood for Bell-Shaped and Triangular Set Functions | |
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| Adaptive Subsethood for Neutral Fuzzy Control with Radial Basis Network | |
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| A Test Case: The Fuzzy Car | |
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| Conclusion | |
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| Appendix 13.A | |
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| References | |
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| Homework Problems | |
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| Feedback in Fuzzy Cubes | |
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| Fuzzy Adaptive Resonance Theory | |
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| Preview | |
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| Match-Based Learning and Error-Based Learning | |
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| ART and Fuzzy Cubes | |
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| ART Dynamics | |
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| Fuzzy ART | |
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| Fuzzy ARTMAP | |
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| Fuzzy ART Algorithm | |
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| Fuzzy ARTMAP Algorithm | |
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| Fuzzy ARTMAP Simulation: Circle-in-the-Square | |
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| ART Applications | |
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| References | |
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| Homework Problems | |
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| Virtual Worlds in Fuzzy Cognitive Maps | |
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| Preview | |
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| Fuzzy Virtual Worlds | |
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| Fuzzy Cognitive Maps | |
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| Virtual Undersea World | |
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| Adaptive Fuzzy Cognitive Maps | |
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| Conclusions | |
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| References | |
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| Homework Problems | |
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| How To Use The Fuzzy Software | |
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| The Fuzzy Function Approximation Software | |
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| The Fuzzy Cognitive Map Software | |
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| Index | |
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| List of Contributors | |