Оглавление
James K. Peckol. Introduction to Fuzzy Logic
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Introduction to Fuzzy Logic
Dedication
Preface. Starting to Think Fuzzy and Beyond
Organizing the Book
The Chapters. Introduction and Background
History and Infrastructure
Sets, Sets, and More Sets
Linguistic Variables and Hedges
Fuzzy Inference and Approximate Reasoning
Doing the Work
Introducing Threshold Logic
Moving to Perceptron Logic
The Appendices
The Audience
Notes to the Instructor
Acknowledgments
About the Author
Introduction. THINGS TO LOOK FOR…
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
Review Questions. Fuzzy Logic
Threshold Logic
Perceptrons
Thought Questions
1 A Brief Introduction and History. THINGS TO LOOK FOR…
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
Example 1.1
Example 1.2
Example 1.3
Example 1.4
1.9 Expert Systems
1.10 Summary
Review Questions
2 A Review of Boolean Algebra. THINGS TO LOOK FOR…
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
2.4.1.2.1 Unary
2.4.1.2.2 Binary
2.4.1.3 Relations
2.5 Implementation
Example 2.1
Example 2.2
Example 2.3
2.6 Logic Minimization
2.6.1 Algebraic Means
Example 2.4
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
3 Crisp Sets and Sets and More Sets. THINGS TO LOOK FOR…
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
Definition 3.1
3.3.2 Basic Classic Crisp Set Properties
Property 3.1 Empty
Property 3.2 Size
Property 3.3 Equal
Property 3.4 Containment
Property 3.5 Union
Property 3.6 Intersection
Property 3.7 Negation
Property 3.8 Commutation
Property 3.9 Associativity
Property 3.10 Distributivity
Property 3.11 Idempotence
Property 3.12 Transitivity
Property 3.13 Excluded Middle
Property 3.14 Contradiction
Property 3.15 De Morgan
3.4 Basic Crisp Applications – A First Step
Example 3.1 A Crisp Activity
3.5 Summary
Review Questions
4 Fuzzy Sets and Sets and More Sets. THINGS TO LOOK FOR…OF THE RESULTING ENTRIES IN THE UNION
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
Definition 4.1
4.6 Fuzzy Membership Functions
Example 4.1 Comparing Fuzzy Subset Membership and Probability Values – Step 1
Example 4.2 Comparing Fuzzy Subset Membership and Probability Values in Figure 4.5 – Step 2
4.7 Fuzzy Set Theory and Operations
4.7.1 Fundamental Terminology
4.7.2 Basic Fuzzy Set Properties and Operations
Property 4.1 Empty
Property 4.2 Size
Property 4.3 Equal
Property 4.4 Containment
Property 4.5 Union
Property 4.6 Intersection
Property 4.7 Negation
Property 4.8 Commutation
Property 4.9 Associativity
Property 4.10 Distributivity
Property 4.11 Idempotence
Property 4.12 Excluded Middle
Property 4.13 Contradiction
Property 4.14 Complement
Property 4.15 De Morgan
Property 4.16 Difference
4.8 Basic Fuzzy Applications – A First Step
4.8.1 A Crisp Activity Revisited
Example 4.3 A Fuzzy Activity – A First Step
Example 4.4 Fuzzy Activity – A Second Step
4.9 Fuzzy Imprecision And Membership Functions
Example 4.5 Crisp vs Fuzzy Using a Graphic Membership Function
4.9.1 Linear Membership Functions
Example 4.6 Basic Linear Membership Function
Example 4.7 Basic Linear Membership Function Linear Up and Linear Down
Example 4.8 Basic Linear Membership Function Linear Up and Down with Offset
Example 4.9 Basic Linear and Bell Shaped Membership Functions – Around Graph
Example 4.10 Basic Linear Membership Functions Around and Restricted Domains
Example 4.11 Membership Function Illustrating a Universe of Discourse
4.9.2 Curved Membership Functions
Example 4.12 Membership Function Illustrating Set of Support
Example 4.13 Membership Function Illustrating Sigmoid Curves
Example 4.14 Membership Function Illustrating the PI Membership Curve
Example 4.15 Membership Function Illustrating the Beta Membership Curve
Example 4.16 Membership Function Illustrating Gaussian Membership Curves
Example 4.17 Using a Graphic Membership Function – 1
Example 4.18 Using a Graphic Membership Function – 2
Example 4.19 Using a Graphic Membership Function – 3
Example 4.20 Using a Graphic Membership Function – 4
Example 4.21 Using a Graphic Membership Function – 5
4.10 Summary
Review Questions
5 What Do You Mean By That? THINGS TO LOOK FOR…
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
Definition 5.0
Definition 5.1
Example 5.0 Combining Hedges
Example 5.1 Combining Hedges
Definition 5.2
Definition 5.3
Definition 5.4
5.4 Summary
Review Questions
6 If There Are Four Philosophers… THINGS TO LOOK FOR…
6.1 Fuzzy Inference and Approximate Reasoning
6.2 Equality
Example 6.1
6.3 Containment and Entailment
Example 6.2
Example 6.3
Example 6.4
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
Example 6.5
Example 6.6
6.4.3 Conditional Relations
Example 6.7
6.4.4 Composition Revisited
6.4.4.1 Max‐Min Composition
6.4.4.2 Max‐Product Composition
Example 6.8
Example 6.9
Example 6.10
6.5 Inference in Fuzzy Logic
6.6 Summary
Review Questions
7 So How Do I Use This Stuff? THINGS TO LOOK FOR…
7.1 Introduction
7.2 Fuzzification and Defuzzification
7.2.1 Fuzzification
7.2.1.1 Graphical Membership Function Features. Core
Boundary
Support
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
Example 7.1
7.6.1 System Behavior
7.6.2 Defuzzification Strategy
7.6.2.1 Test Case
Example 7.2
7.6.3 Membership Functions
7.6.4 System Behavior
7.6.4.1 Defuzzification Strategy
7.7 Summary
Review Questions
8 I Can Do This Stuff!!! THINGS TO LOOK FOR…
8.1 Introduction
8.2 Applications
8.3 Design Methodology
8.4 Executing a Design Methodology
8.5 Summary
Review Questions
9 Moving to Threshold Logic!!! THINGS TO LOOK FOR…
9.1 Introduction
9.2 Threshold Logic
9.3 Executing a Threshold Logic Design
9.3.1 Designing an AND Gate
9.3.2 Designing an OR Gate
9.3.3 Designing a Fundamental Boolean Function
9.4 The Downfall of Threshold Logic Design
9.5 Summary
Review Questions
10 Moving to Perceptron Logic ! ! ! THINGS TO LOOK FOR…
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
Example 10.1 The Basic Logic Gates
Example 10.2 Adding Weights
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
Example 10.3 Common Activation Transfer Functions
10.5 Learning with Perceptrons – First Step
Terminology
10.5.1 Learning with Perceptrons – The Learning Rule
Example 10.4 Simple Learning Example 1
Example 10.5 Simple Learning Example 2
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
A Requirements and Design Specification. THINGS TO LOOK FOR…
A.1 Introduction
Stating the Problem
Example A.1 Designing a Counter
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.3.2.1.1 System Inputs and Outputs
A.3.2.1.2 Functional View
A.3.2.1.3 Operational View
A.3.2.1.4 Technological View
A.3.2.1.5 Safety, Security, and Reliability
Example A.2 Identifying the Requirements
A.4 The System Design Specification
A.4.1 The System
A.4.2 Quantifying the System
Example A.3 Quantifying the Specification
A.5 System Requirements Versus System Design Specifications
B Introduction to UML and Thinking Test. THINGS TO LOOK FOR…
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.10.2.6 History States
B.10.2.7 Concurrent Substates
B.10.2.8 Data Source/Sink
B.10.2.9 Data Store
Example B.1
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
Further Reading. HOW CAN I LEARN MORE?
Index. a
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