Description
Book SynopsisLearn more about the history, foundations, and applications of fuzzy logic in this comprehensive resource by an academic leader Introduction to Fuzzy Logic delivers a high-level but accessible introduction to the rapidly growing and evolving field of fuzzy logic and its applications. Distinguished engineer, academic, and author James K. Peckol covers a wide variety of practical topics, including the differences between crisp and fuzzy logic, the people and professions who find fuzzy logic useful, and the advantages of using fuzzy logic. While the book assumes a solid foundation in embedded systems, including basic logic design, and C/C++ programming, it is written in a practical and easy-to-read style that engages the reader and assists in learning and retention. The author includes introductions of threshold and perceptron logic to further enhance the applicability of the material contained within. After introducing readers to the topic with a brief description of the history and development of the field, Introduction to Fuzzy Logic goes on to discuss a wide variety of foundational and advanced topics, like: A review of Boolean algebra, including logic minimization with algebraic means and Karnaugh mapsA discussion of crisp sets, including classic set membership, set theory and operations, and basic classical crisp set propertiesA discussion of fuzzy sets, including the foundations of fuzzy sets logic, set membership functions, and fuzzy set propertiesAn analysis of fuzzy inference and approximate reasoning, along with the concepts of containment and entailment and relations between fuzzy subsetsPerfect for mid-level and upper-level undergraduate and graduate students in electrical, mechanical, and computer engineering courses, Introduction to Fuzzy Logic covers topics included in many artificial intelligence, computational intelligence, and soft computing courses. Math students and professionals in a wide variety of fields will also significantly benefit from the material covered in this book.
Table of ContentsPreface (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
