INTRODUCTION TO FUZZY LOGIC
Learn 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 professionals 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 maps
A discussion of crisp sets, including classic set membership, set theory and operations, and basic classical crisp set properties
A discussion of fuzzy sets, including the foundations of fuzzy set logic, set membership functions, and fuzzy set properties
An analysis of fuzzy inference and approximate reasoning, along with the concepts of containment and entailment and relations between fuzzy subsets
Perfect 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.
Author(s): James K. Peckol
Edition: 1
Publisher: Wiley
Year: 2021
Language: English
Pages: 304
Tags: fuzzy, logic
Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgments
About the Author
Introduction
I.1 Introducing Fuzzy Logic, Fuzzy Systems, and • • • • •
I.2 Philosophy
I.3 Starting to Think Fuzzy – Fuzzy Logic Q&A
I.4 Is Fuzzy Logic a Relatively New Technology?
I.5 Who Is Using Fuzzy Logic in the United States?
I.6 What Are Some Advantages of Fuzzy Logic?
I.7 Can I Use Fuzzy Logic to Solve All My Design Problems?
I.8 What’s Wrong with the Tools I’m Using Now?
I.9 Should I Implement My Fuzzy System in Hardware or Software?
I.10 Introducing Threshold Logic
I.11 Moving to Perceptron Logic
I.12 Testing and Debugging
I.13 Summary
Chapter 1 A Brief Introduction and History
1.1 Introduction
1.2 Models of Human Reasoning
1.2.1 The Early Foundation
1.2.1.1 Three Laws of Thought
1.3 Building on the Past – From Those Who Laid the Foundation
1.4 A Learning and Reasoning Taxonomy
1.4.1 Rote Learning
1.4.2 Learning with a Teacher
1.4.3 Learning by Example
1.4.4 Analogical or Metaphorical Learning
1.4.5 Learning by Problem Solving
1.4.6 Learning by Discovery
1.5 Crisp and Fuzzy Logic
1.6 Starting to Think Fuzzy
1.7 History Revisited – Early Mathematics
1.7.1 Foundations of Fuzzy Logic
1.7.2 Fuzzy Logic and Approximate Reasoning
1.7.3 Non-monotonic Reasoning
1.8 Sets and Logic
1.8.1 Classical Sets
1.8.2 Fuzzy Subsets
1.8.3 Fuzzy Membership Functions
1.9 Expert Systems
1.10 Summary
Review Questions
Chapter 2 A Review of Boolean Algebra
2.1 Introduction to Crisp Logic and Boolean Algebra
2.2 Introduction to Algebra
2.2.1 Postulates
2.2.2 Theorems
2.3 Getting Some Practice
2.4 Getting to Work
2.4.1 Boolean Algebra
2.4.1.1 Operands
2.4.1.2 Operators
2.4.1.3 Relations
2.5 Implementation
2.6 Logic Minimization
2.6.1 Algebraic Means
2.6.2 Karnaugh Maps
2.6.2.1 Applying the K-Map
2.6.2.2 Two-Variable K-Maps
2.6.2.3 Three-Variable K-Maps
2.6.2.4 Four-Variable K-Maps
2.6.2.5 Going Backward
2.6.2.6 Don’t Care Variables
2.7 Summary
Review Questions
Chapter 3 Crisp Sets and Sets and More Sets
3.1 Introducing the Basics
3.2 Introduction to Classic Sets and Set Membership
3.2.1 Classic Sets
3.2.2 Set Membership
3.2.3 Set Operations
3.2.4 Exploring Sets and Set Membership
3.2.5 Fundamental Terminology
3.2.6 Elementary Vocabulary
3.3 Classical Set Theory and Operations
3.3.1 Classical Set Logic
3.3.2 Basic Classic Crisp Set Properties
3.4 Basic Crisp Applications – A First Step
3.5 Summary
Review Questions
Chapter 4 Fuzzy Sets and Sets and More Sets
4.1 Introducing Fuzzy
4.2 Early Mathematics
4.3 Foundations of Fuzzy Logic
4.4 Introducing the Basics
4.5 Introduction to Fuzzy Sets and Set Membership
4.5.1 Fuzzy Subsets and Fuzzy Logic
4.6 Fuzzy Membership Functions
4.7 Fuzzy Set Theory and Operations
4.7.1 Fundamental Terminology
4.7.2 Basic Fuzzy Set Properties and Operations
4.8 Basic Fuzzy Applications – A First Step
4.8.1 A Crisp Activity Revisited
4.9 Fuzzy Imprecision And Membership Functions
4.9.1 Linear Membership Functions
4.9.2 Curved Membership Functions
4.10 Summary
Review Questions
Chapter 5 What Do You Mean By That?
5.1 Language, Linguistic Variables, Sets, and Hedges
5.2 Symbols and Sounds to Real-World Objects
5.2.1 Crisp Sets – a Second Look
5.2.2 Fuzzy Sets – a Second Look
5.2.2.1 Linguistic Variables
5.2.2.2 Membership Functions
5.3 Hedges
5.4 Summary
Review Questions
Chapter 6 If There Are Four Philosophers. . .
6.1 Fuzzy Inference and Approximate Reasoning
6.2 Equality
6.3 Containment and Entailment
6.4 Relations Between Fuzzy Subsets
6.4.1 Union and Intersection
6.4.1.1 Union
6.4.1.2 Intersection
6.4.2 Conjunction and Disjunction
6.4.3 Conditional Relations
6.4.4 Composition Revisited
6.5 Inference in Fuzzy Logic
6.6 Summary
Review Questions
Chapter 7 So How Do I Use This Stuff?
7.1 Introduction
7.2 Fuzzification and Defuzzification
7.2.1 Fuzzification
7.2.1.1 Graphical Membership Function Features
7.2.2 Defuzzification
7.3 Fuzzy Inference Revisited
7.3.1 Fuzzy Implication
7.4 Fuzzy Inference – Single Premise
7.4.1 Max Criterion
7.4.2 Mean of Maximum
7.4.3 Center of Gravity
7.5 Fuzzy Inference – Multiple Premises
7.6 Getting to Work – Fuzzy Control and Fuzzy Expert Systems
7.6.1 System Behavior
7.6.2 Defuzzification Strategy
7.6.2.1 Test Case
7.6.3 Membership Functions
7.6.4 System Behavior
7.6.4.1 Defuzzification Strategy
7.7 Summary
Review Questions
Chapter 8 I Can Do This Stuff!!!
8.1 Introduction
8.2 Applications
8.3 Design Methodology
8.4 Executing a Design Methodology
8.5 Summary
Review Questions
Chapter 10 Moving to Perceptron Logic ! ! !
10.1 Introduction
10.2 The Biological Neuron
10.2.1 Dissecting the Biological Neuron
10.2.1.1 Dendrites
10.2.1.2 Cell Body – Soma
10.2.1.3 Axon – Myelin Sheath
10.2.1.4 Synapse
10.3 The Artificial Neuron – a First Step
10.4 The Perceptron – The Second Step
10.4.1 The Basic Perceptron
10.4.2 Single– and Multilayer Perceptron
10.4.3 Bias and Activation Function
10.5 Learning with Perceptrons – First Step
Terminology
10.5.1 Learning with Perceptrons – The Learning Rule
10.6 Learning with Perceptrons – Second Step
10.6.1 Path of the Perceptron Inputs
10.6.1.1 Implementation/Execution Concerns
10.7 Testing of the Perceptron
10.8 Summary
Review Questions
Appendix A Requirements and Design Specification
A.1 Introduction
A.2 Identifying the Requirements
A.3 Formulating the Requirements Specification
A.3.1 The Environment
A.3.1.1 Characterizing External Entities
A.3.2 The System
A.3.2.1 Characterizing the System
A.4 The System Design Specification
A.4.1 The System
A.4.2 Quantifying the System
A.5 System Requirements Versus System Design Specifications
Appendix B Introduction to UML and Thinking Test
B.1 Introduction
B.2 Use Cases
B.2.1 Writing a Use Case
B.3 Class Diagrams
B.3.1 Class Relationships
B.3.1.1 Inheritance or Generalization
B.3.1.2 Interface
B.3.1.3 Containment
B.3.1.4 Aggregation
B.3.1.5 Composition
B.4 Dynamic Modeling with UML
B.5 Interaction Diagrams
B.5.1 Call and Return
B.5.2 Create and Destroy
B.5.2.1 Send
B.6 Sequence Diagrams
B.7 Fork and Join
B.8 Branch and Merge
B.9 Activity Diagram
B.10 State Chart Diagrams
B.10.1 Events
B.10.2 State Machines and State Chart Diagrams
B.10.2.1 UML State Chart Diagrams
B.10.2.2 Transitions
B.10.2.3 Guard Conditions
B.10.2.4 Composite States
B.10.2.5 Sequential States
B.10.2.7 Concurrent Substates
B.10.2.8 Data Source/Sink
B.10.2.9 Data Store
B.11 Preparing for Test
B.11.1 Thinking Test
B.11.2 Examining the Environment
B.11.2.1 Test Equipment
B.11.2.2 The Eye Diagram
B.11.2.3 Generating the Eye Diagram
B.11.2.4 Interpreting the Eye Diagram
B.11.3 Back of the Envelope Examination
B.11.3.1 A First Step Check List
B.11.4 Routing and Topology
B.12 Summary
Bibliography
Index
EULA
