Fuzzy Logic with Engineering Applications

Timothy J. Ross, University of New Mexico, USADr. Ross is a professor within the Department of Civil Engineering at the University of New Mexico where he teaches courses in structural analysis, structural dynamics and fuzzy logic. He is a registered professional engineer with over 30 years’ experience in the fields of computational mechanics, hazard survivability, structural dynamics, structural safety, stochastic processes, risk assessment, and fuzzy systems. He is also the founding Editor-in-Chief of the International Journal, Intelligent and Fuzzy Systems.

• About the Author xiPreface to the Fourth Edition xiii1 Introduction 1The Case for Imprecision 2A Historical Perspective 4The Utility of Fuzzy Systems 7Limitations of Fuzzy Systems 9The Illusion: Ignoring Uncertainty and Accuracy 11Uncertainty and Information 13Fuzzy Sets and Membership 14Chance versus Fuzziness 17Intuition of Uncertainty: Fuzzy versus Probability 19Sets as Points in Hypercubes 21Summary 23References 23Problems 242 Classical Sets and Fuzzy Sets 27Classical Sets 28Fuzzy Sets 36Summary 45References 46Problems 463 Classical Relations and Fuzzy Relations 51Cartesian Product 52Crisp Relations 53Fuzzy Relations 58Tolerance and Equivalence Relations 67Fuzzy Tolerance and Equivalence Relations 70Value Assignments 72Other Forms of the Composition Operation 76Summary 77References 77Problems 774 Properties of Membership Functions, Fuzzification, and Defuzzification 84Features of the Membership Function 85Various Forms 87Fuzzification 88Defuzzification to Crisp Sets 90λ-Cuts for Fuzzy Relations 92Defuzzification to Scalars 93Summary 102References 103Problems 1045 Logic and Fuzzy Systems 107Part I: Logic 107Classical Logic 108Fuzzy Logic 122Part II: Fuzzy Systems 132Summary 151References 153Problems 1546 Historical Methods of Developing Membership Functions 163Membership Value Assignments 164Intuition 164Inference 165Rank Ordering 167Neural Networks 168Genetic Algorithms 179Inductive Reasoning 188Summary 195References 196Problems 1977 Automated Methods for Fuzzy Systems 201Definitions 202Batch Least Squares Algorithm 205Recursive Least Squares Algorithm 210Gradient Method 213Clustering Method 218Learning from Examples 221Modified Learning from Examples 224Summary 233References 235Problems 2358 Fuzzy Systems Simulation 237Fuzzy Relational Equations 242Nonlinear Simulation Using Fuzzy Systems 243Fuzzy Associative Memories (FAMs) 246Summary 257References 258Problems 2599 Decision Making with Fuzzy Information 265Fuzzy Synthetic Evaluation 267Fuzzy Ordering 269Nontransitive Ranking 272Preference and Consensus 275Multiobjective Decision Making 279Fuzzy Bayesian Decision Method 285Decision Making under Fuzzy States and Fuzzy Actions 295Summary 309References 310Problems 31110 Fuzzy Classification and Pattern Recognition 323Fuzzy Classification 324Classification by Equivalence Relations 324Cluster Analysis 332Cluster Validity 332c-Means Clustering 333Hard c-Means (HCM) 333Fuzzy c-Means (FCM) 343Classification Metric 351Hardening the Fuzzy c-Partition 354Similarity Relations from Clustering 356Fuzzy Pattern Recognition 357Single-Sample Identification 357Multifeature Pattern Recognition 365Summary 378References 379Problems 38011 Fuzzy Control Systems 388Control System Design Problem 390Examples of Fuzzy Control System Design 393Fuzzy Engineering Process Control 404Fuzzy Statistical Process Control 417Industrial Applications 431Summary 434References 437Problems 43812 Applications of Fuzzy Systems Using Miscellaneous Models 455Fuzzy Optimization 455Fuzzy Cognitive Mapping 462Agent-Based Models 477Fuzzy Arithmetic and the Extension Principle 481Fuzzy Algebra 487Data Fusion 491Summary 498References 498Problems 50013 Monotone Measures: Belief, Plausibility, Probability, and Possibility 505Monotone Measures 506Belief and Plausibility 507Evidence Theory 512Probability Measures 515Possibility and Necessity Measures 517Possibility Distributions as Fuzzy Sets 525Possibility Distributions Derived from Empirical Intervals 528Summary 548References 549Problems 550Index 554