Documentation Table of Contents

Introduction

• Fuzzy Logic
• The Manual
• The Demonstration Notebooks
• The Packages
• Loading the Package
• Getting More Information about Mathematica
• Getting More Information about Fuzzy Sets
• Acknowledgments
• About the Authors

New Features in This Release

• Introduction
• New Membership Functions
• Fuzzy Graph
• Defuzzifications
• Additional Operators
• New Intersections and Unions
• Alpha Cuts for Fuzzy Relations
• Fuzzy Relation Equations
• Random Fuzzy Sets and Fuzzy Relations
• Fuzzy Inferencing
• Fuzzy Arithmetic
• Fuzzy Clustering

Part 1: Manual

1. Creating Fuzzy Sets

• Introduction
• Basic Objects
• Functions for Creating Fuzzy Sets

2. Creating Fuzzy Relations

• Introduction
• Basic Objects
• Functions for Creating Fuzzy Relations

3. Fuzzy Operations

• Introduction
• Fuzzy Set Operations
• Fuzzy Relation Operations
• Fuzzy Set or Fuzzy Relation Operations

4. Aggregation Operations

• Introduction
• Intersection (T-Norm) and Union (S-Norm) Operations
• Averaging Operations
• Difference Operations
• User-Defined Aggregators

5. Fuzzy Set Visualization

• Introduction
• Visualization Functions

6. Fuzzy Relation Visualization

• Introduction
• Visualization Functions

7. Compositions

• Introduction
• Composition Function

8. Fuzzy Inferencing

• Introduction
• Inference Functions
• Composition-Based Inference
• Rule-Based Inference

9. Fuzzy Arithmetic

• Introduction
• Fuzzy Arithmetic Functions

10. Discrete Fuzzy Arithmetic

• Introduction
• Discrete Arithmetic on Triangular Fuzzy Numbers
• Discrete Arithmetic on Gaussian Fuzzy Numbers

11. Lukasiewicz Sets and Logic

• Introduction
• Creating Lukasiewicz Sets
• Operations on LN Sets

12. Fuzzy Clustering

• Introduction
• Fuzzy C-Means Clustering (FCM)
• Example

Appendix

• Fuzzy Operator Formulas
• Intersection Formulas
• Union Formulas
• Averaging Formulas
• Miscellaneous Formulas

Bibliography

Part 2: Demonstration Notebooks

1. Sets versus Fuzzy Sets

• Introduction
• Characteristic Function and Membership Function
• Graphic Interpretation of Sets
• References

2. Standard Operations

• Introduction
• Fuzzy Operations
• References

3. Fuzzy Relations

• Introduction
• Fuzzy Relation Form
• Projection of a Fuzzy Relation
• Fuzzy Operations
• Composition of Two Fuzzy Relations
• Binary Relations
• References

4. Fuzzy Modeling

• Introduction
• Representing the Model Input
• Representing the Model Output
• Creating Linguistic Control Rules
• Building the Model
• Using the Model
• Evaluating the Model
• References

5. Fuzzy Logic Control

• Introduction
• Defining Input Membership Functions
• Defining Output Membership Functions
• Defining Control Rules
• Simulation Functions
• Test Run 1
• Test Run 2
• Control Surface
• References

6. Fuzzy Numbers

• Introduction
• Creating Fuzzy Numbers
• Fuzzy Arithmetic
• References

7. Digital Fuzzy Sets and Multivalued Logic

• Introduction
• Creating Digital Fuzzy Sets
• Lukasiewicz Multivalued Logic
• References

8. Additional Examples

• Introduction
• Example 1: Classifying Houses
• Example 2: Representing Age
• Example 3: Finding the Disjunctive Sum
• Example 4: Natural Numbers
• Example 5: Fuzzy Hedges
• Example 6: Distance Relation
• Example 7: Choosing a Job
• Example 8: Digital Fuzzy Sets
• Example 9: Image Processing
• References

Index