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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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Preview | |
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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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Preview | |
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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 | |