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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

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