Fuzzy Logic with Engineering Applications

About the Author Preface to the Third Edition 1 Introduction The Case for Imprecision A Historical Perspective The Utility of Fuzzy Systems Limitations of Fuzzy Systems The Illusion: Ignoring Uncertainty and Accuracy Uncertainty and Information The Unknown Fuzzy Sets and Membership Chance Versus Fuzziness Sets as Points in Hypercubes Summary References Problems 2 Classical Sets and Fuzzy Sets Classical Sets Operations on Classical Sets Properties of Classical (Crisp) Sets Mapping of Classical Sets to Functions Fuzzy Sets Fuzzy Set Operations Properties of Fuzzy Sets Alternative Fuzzy Set Operations Summary References Problems 3 Classical Relations and Fuzzy Relations Cartesian Product Crisp Relations Cardinality of Crisp Relations Operations on Crisp Relations Properties of Crisp Relations Composition Fuzzy Relations Cardinality of Fuzzy Relations Operations on Fuzzy Relations Properties of Fuzzy Relations Fuzzy Cartesian Product and Composition Tolerance and Equivalence Relations Crisp Equivalence Relation Crisp Tolerance Relation Fuzzy Tolerance and Equivalence Relations Value Assignments Cosine Amplitude Max-Min Method Other Similarity Methods Other Forms of the Composition Operation Summary References Problems 4 Properties of Membership Functions, Fuzzification, and Defuzzification Features of the Membership Function Various Forms Fuzzification Defuzzification to Crisp Sets "-Cuts for Fuzzy Relations Defuzzification to Scalars Summary References Problems 5 Logic and Fuzzy Systems Part I Logic Classical Logic Proof Fuzzy Logic Approximate Reasoning Other Forms of the Implication Operation Part II Fuzzy Systems Natural Language Linguistic Hedges Fuzzy (Rule-Based) Systems Graphical Techniques of Inference Summary References Problems 6 Development of Membership Functions Membership Value Assignments Intuition Inference Rank Ordering Neural Networks Genetic Algorithms Inductive Reasoning Summary References Problems 7 Automated Methods for Fuzzy Systems Definitions Batch Least Squares Algorithm Recursive Least Squares Algorithm Gradient Method Clustering Method Learning From Examples Modified Learning From Examples Summary References Problems 8 Fuzzy Systems Simulation Fuzzy Relational Equations Nonlinear Simulation Using Fuzzy Systems Fuzzy Associative Memories (FAMS) Summary References Problems 9 Decision Making with Fuzzy Information Fuzzy Synthetic Evaluation Fuzzy Ordering Nontransitive Ranking Preference and Consensus Multiobjective Decision Making Fuzzy Bayesian Decision Method Decision Making Under Fuzzy States and Fuzzy Actions Summary References Problems 10 Fuzzy Classification Classification by Equivalence Relations Crisp Relations Fuzzy Relations Cluster Analysis Cluster Validity c-Means Clustering Hard c-Means (HCM) Fuzzy c-Means (FCM) Fuzzy c-Means Algorithm Classification Metric Hardening the Fuzzy c-Partition Similarity Relations from Clustering Summary References Problems 11 Fuzzy Pattern Recognition Feature Analysis Partitions of the Feature space Single-Sample Identification Multifeature Pattern Recognition Image Processing Summary References Problems 12 Fuzzy Arithmetic and the Extension Principle Extension Principle Crisp Functions, Mapping, and Relations Functions of Fuzzy Sets - Extension Principle Fuzzy Transform (Mapping) Practical Considerations Fuzzy Arithmetic Interval Analysis in Arithmetic Approximate Methods of Extension Vertex Method DSW Algorithm Restricted DSW Algorithm Comparisons Summary References Problems 13 Fuzzy Control Systems Control System Design Problem Control (Decision) Surface Assumptions in a Fuzzy Control System Design Simple Fuzzy Logic Controllers Examples of Fuzzy Control System Design Aircraft Landing Control Problem Fuzzy Engineering Process Control Classical Feedback Control Fuzzy Control Fuzzy Statistical Process Control Measurement Data - Traditional SPC Attribute Data - Traditional SPC Industrial Applications Summary References Problems 14 Miscellaneous Topics Fuzzy Optimization One-Dimensional Optimization Fuzzy Cognitive Mapping Concept Variables and Causal Relations Fuzzy Cognitive Maps Agent-Based Models Summary References Problems 15 Monotone Measures: Belief, Plausibility, Probability,and Possibility Monotone Measures Belief and Plausibility Evidence Theory Probability Measures Possibility and Necessity Measures Possibility Distributions as Fuzzy Sets Possibility Distributions Derived from Empirical Intervals Deriving Possibility Distributions from Overlapping Intervals Redistributing Weight from Nonconsonant to Consonant Intervals Comparison of Possibility Theory and Probability Theory Summary References Problems Index