Introduction to Fuzzy Logic

ISBN-13: 9781119772613 / Angielski / Twarda / 2021 / 304 str.

James K. Peckol

Spis treści

Preface (1-11)Acknowledgements ( 1 )About the Author ( 1 )IntroductionChapter 1 A Brief Introduction and History 1Introduction 1Models of Human Reasoning 1The Early Foundation 2Building On The Past - From Those Who Laid The Foundation 3A Learning and Reasoning Taxonomy 4Rote Learning 4Learning With a Teacher 5Learning by Example 5Analogical or Metaphorical Learning 6Learning by Problem Solving 6Learning By Discovery 7Crisp and Fuzzy Logic 7Starting To Think Fuzzy 7History Revisited - Early Mathematics 9Foundations of Fuzzy Logic 9Fuzzy Logic And Approximate Reasoning 9Non-Monotonic Reasoning 11Sets and Logic 12Classical Sets 12Fuzzy Subsets 13Fuzzy Membership Functions 14Expert Systems 16Summary 17Review questions 17Chapter 2 A Review of Boolean Algebra 19Introduction to crisp logic and Boolean Algebra 19Introduction to algebra 20Postulates 20Theorems 23Getting some practice 24Getting to work 24Boolean Algebra 24Implementation 28Logic minimization 29Algebraic Means 29Karnaugh Maps 30Applying the K-map 302 Variable K-Maps 313 Variable K-Maps 324 Variable K-Maps 33Going Backwards 33Don't Care Variables 35Summary 37Review questions 37Chapter 3 Crisp Sets and Sets and More Sets 38Introducing the Basics 38Introduction to Classic Sets and Set Membership 41Classic Sets 41Set Membership 41Basic Classic Crisp Set Properties 45Exploring Sets and Set Membership 46Fundamental Terminology 47Elementary Vocabulary 47Classical Set Theory and Operations 49Classic Set Logic 49Basic Classical Crisp Set Properties 50Basic Crisp Applications - A First Step 57Summary 59Review questions 60Chapter 4 Fuzzy Sets and Sets and More Sets 61Introducing Fuzzy 61Early Mathematics 62Foundations of Fuzzy Sets Logic 62Introducing the Basics 64Introduction to Fuzzy Sets and Set Membership 66Fuzzy Subsets and Fuzzy Logic 66Fuzzy Membership Functions 68Fuzzy Set Theory and Operations 71Fundamental Terminology 71Basic Fuzzy Set Properties and Operations 72Basic Fuzzy Applications - A First Step 83A Crisp Activity revisited 83Fuzzy Imprecision and Membership Functions 86Linear Membership Functions 87Curved Membership Functions 90Summary 95Review questions 96Chapter 5 What do You Mean by That? 97Language, Linguistic Variables, Sets And Hedges 97Symbols And Sounds To Real World Objects 99Crisp Sets a Second Look 99Fuzzy Sets a Second Look 103Linguistic Variables 103Membership Functions 105Hedges 106Summary 110Review questions 111Chapter 6 If There Were Four Philosophers 112Fuzzy Inference And Approximate Reasoning 112Equality 113Containment And Entailment 116Relations Between Fuzzy Subsets 119Union and Intersection 119Conjunction and Disjunction 121Conditional Relations 125Composition Revisited 127Max-Min Composition 128Max-Product Composition 130Inference In Fuzzy Logic 137Summary 140Review questions 141Chapter 7 So How Do I Use This Stuff? 142Introduction 142Fuzzification and Defuzzification 143Fuzzification 143Defuzzification 146Fuzzy Inference Revisited 147Fuzzy Implication 148Fuzzy Inference - Single Premise 149Max Criterion 150Mean of Maximum 151Center of Gravity 152Fuzzy Inference - Multiple Premises 153Getting to work - Fuzzy Control and Fuzzy Expert Systems 154Membership Functions 158System Behavior 159Defuzzification Strategy 160Membership Functions 162System Behavior 163Defuzzification Strategy 164Summary 165Review questions 166Chapter 8 I Can Do This Stuff !!! 167Introduction 167Applications 167Design Methodology 168Executing a Design Methodology 169Summary 172Review questions 172Chapter 9 Moving to Threshold Logic !!! 173Introduction 173Threshold Logic 173Executing a Threshold Logic Design 174Designing an AND Gate 175Designing an OR Gate 175Designing a Fundamental Boolean Function 176The Downfall of Threshold Logic Design 179Summary 180Review Questions 181Chapter 10 Moving to Perceptron Logic !!! 182Introduction 182The Biological Neuron 183Dissecting the Biological Neuron 184The Artificial Neuron - A First Step 185The Perceptron - The Second Step 189The Basic Perceptron 190Single and Multilayer Perceptron 192Bias and Activation Function 193Learning with Perceptrons - First Step 196Learning with Perceptrons - The Learning Rule 197Learning with Perceptrons -Second Step 200Path of the Perceptron Inputs 201Testing of the Perceptron 203Summary 204Review Questions 205Appendix A Requirements and Design Specifications 207Introduction 207Identifying the requirements 209Formulating the requirements specification 211The Environment 212Characterizing External Entities 212The System 213Characterizing the System 214System Inputs And Outputs 214Functional View 215Operational View 215Technological View 215Safety, Security, And Reliability 216The System Design Specification 223The System 225Quantifying the System 225System Requirements Versus System Design Specifications 335Appendix B Introduction to UML 237Introduction 237Use Cases 238Writing a Use Case 240Class Diagrams 241Class Relationships 242Inheritance or Generalization 242Interface 243Containment 243Aggregation 243Composition 244Dynamic Modeling with UML 245Interaction Diagrams 245Call and Return 246Create and Destroy 246Send 247Sequence diagrams 247Fork and join 248Branch and merge 249Activity diagram 250State chart diagrams 251Events 251State Machines and State Chart Diagrams 252UML State Chart Diagrams 252Transitions 253Guard Conditions 253Composite States 254Sequential States 254History States 255Concurrent Substates 255Data Source / Sink 256Data Store 256Preparing for Test 258Thinking Test 258Examining the Environment 259Test Equipment 259The Eye Diagram 260Generating the Eye Diagram 260Interpreting the Eye Diagram 261Back of the Envelope Examination 262A First Step Check List 262Routing and Topology 263Summary 263BibliographyIndex

O autorze

James K. Peckol, PhD, is Principal Lecturer Emeritus in the Department of Electrical and Computer Engineering at the University of Washington in Seattle. He has over 50 years of experience in engineering and education in the fields of software, digital, medical, and embedded systems design and development.