Introduction to 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