Introduction to Fuzzy Logic

Preface (1-11) Acknowledgements ( 1 ) About the Author ( 1 ) Introduction Chapter 1 A Brief Introduction and History 1 Introduction 1 Models of Human Reasoning 1 The Early Foundation 2 Building On The Past - From Those Who Laid The Foundation 3 A Learning and Reasoning Taxonomy 4 Rote Learning 4 Learning With a Teacher 5 Learning by Example 5 Analogical or Metaphorical Learning 6 Learning by Problem Solving 6 Learning By Discovery 7 Crisp and Fuzzy Logic 7 Starting To Think Fuzzy 7 History Revisited - Early Mathematics 9 Foundations of Fuzzy Logic 9 Fuzzy Logic And Approximate Reasoning 9 Non-Monotonic Reasoning 11 Sets and Logic 12 Classical Sets 12 Fuzzy Subsets 13 Fuzzy Membership Functions 14 Expert Systems 16 Summary 17 Review questions 17 Chapter 2 A Review of Boolean Algebra 19 Introduction to crisp logic and Boolean Algebra 19 Introduction to algebra 20 Postulates 20 Theorems 23 Getting some practice 24 Getting to work 24 Boolean Algebra 24 Implementation 28 Logic minimization 29 Algebraic Means 29 Karnaugh Maps 30 Applying the K-map 30 2 Variable K-Maps 31 3 Variable K-Maps 32 4 Variable K-Maps 33 Going Backwards 33 Don't Care Variables 35 Summary 37 Review questions 37 Chapter 3 Crisp Sets and Sets and More Sets 38 Introducing the Basics 38 Introduction to Classic Sets and Set Membership 41 Classic Sets 41 Set Membership 41 Basic Classic Crisp Set Properties 45 Exploring Sets and Set Membership 46 Fundamental Terminology 47 Elementary Vocabulary 47 Classical Set Theory and Operations 49 Classic Set Logic 49 Basic Classical Crisp Set Properties 50 Basic Crisp Applications - A First Step 57 Summary 59 Review questions 60 Chapter 4 Fuzzy Sets and Sets and More Sets 61 Introducing Fuzzy 61 Early Mathematics 62 Foundations of Fuzzy Sets Logic 62 Introducing the Basics 64 Introduction to Fuzzy Sets and Set Membership 66 Fuzzy Subsets and Fuzzy Logic 66 Fuzzy Membership Functions 68 Fuzzy Set Theory and Operations 71 Fundamental Terminology 71 Basic Fuzzy Set Properties and Operations 72 Basic Fuzzy Applications - A First Step 83 A Crisp Activity revisited 83 Fuzzy Imprecision and Membership Functions 86 Linear Membership Functions 87 Curved Membership Functions 90 Summary 95 Review questions 96 Chapter 5 What do You Mean by That? 97 Language, Linguistic Variables, Sets And Hedges 97 Symbols And Sounds To Real World Objects 99 Crisp Sets a Second Look 99 Fuzzy Sets a Second Look 103 Linguistic Variables 103 Membership Functions 105 Hedges 106 Summary 110 Review questions 111 Chapter 6 If There Were Four Philosophers 112 Fuzzy Inference And Approximate Reasoning 112 Equality 113 Containment And Entailment 116 Relations Between Fuzzy Subsets 119 Union and Intersection 119 Conjunction and Disjunction 121 Conditional Relations 125 Composition Revisited 127 Max-Min Composition 128 Max-Product Composition 130 Inference In Fuzzy Logic 137 Summary 140 Review questions 141 Chapter 7 So How Do I Use This Stuff? 142 Introduction 142 Fuzzification and Defuzzification 143 Fuzzification 143 Defuzzification 146 Fuzzy Inference Revisited 147 Fuzzy Implication 148 Fuzzy Inference - Single Premise 149 Max Criterion 150 Mean of Maximum 151 Center of Gravity 152 Fuzzy Inference - Multiple Premises 153 Getting to work - Fuzzy Control and Fuzzy Expert Systems 154 Membership Functions 158 System Behavior 159 Defuzzification Strategy 160 Membership Functions 162 System Behavior 163 Defuzzification Strategy 164 Summary 165 Review questions 166 Chapter 8 I Can Do This Stuff !!! 167 Introduction 167 Applications 167 Design Methodology 168 Executing a Design Methodology 169 Summary 172 Review questions 172 Chapter 9 Moving to Threshold Logic !!! 173 Introduction 173 Threshold Logic 173 Executing a Threshold Logic Design 174 Designing an AND Gate 175 Designing an OR Gate 175 Designing a Fundamental Boolean Function 176 The Downfall of Threshold Logic Design 179 Summary 180 Review Questions 181 Chapter 10 Moving to Perceptron Logic !!! 182 Introduction 182 The Biological Neuron 183 Dissecting the Biological Neuron 184 The Artificial Neuron - A First Step 185 The Perceptron - The Second Step 189 The Basic Perceptron 190 Single and Multilayer Perceptron 192 Bias and Activation Function 193 Learning with Perceptrons - First Step 196 Learning with Perceptrons - The Learning Rule 197 Learning with Perceptrons -Second Step 200 Path of the Perceptron Inputs 201 Testing of the Perceptron 203 Summary 204 Review Questions 205 Appendix A Requirements and Design Specifications 207 Introduction 207 Identifying the requirements 209 Formulating the requirements specification 211 The Environment 212 Characterizing External Entities 212 The System 213 Characterizing the System 214 System Inputs And Outputs 214 Functional View 215 Operational View 215 Technological View 215 Safety, Security, And Reliability 216 The System Design Specification 223 The System 225 Quantifying the System 225 System Requirements Versus System Design Specifications 335 Appendix B Introduction to UML 237 Introduction 237 Use Cases 238 Writing a Use Case 240 Class Diagrams 241 Class Relationships 242 Inheritance or Generalization 242 Interface 243 Containment 243 Aggregation 243 Composition 244 Dynamic Modeling with UML 245 Interaction Diagrams 245 Call and Return 246 Create and Destroy 246 Send 247 Sequence diagrams 247 Fork and join 248 Branch and merge 249 Activity diagram 250 State chart diagrams 251 Events 251 State Machines and State Chart Diagrams 252 UML State Chart Diagrams 252 Transitions 253 Guard Conditions 253 Composite States 254 Sequential States 254 History States 255 Concurrent Substates 255 Data Source / Sink 256 Data Store 256 Preparing for Test 258 Thinking Test 258 Examining the Environment 259 Test Equipment 259 The Eye Diagram 260 Generating the Eye Diagram 260 Interpreting the Eye Diagram 261 Back of the Envelope Examination 262 A First Step Check List 262 Routing and Topology 263 Summary 263 Bibliography Index