Fuzzy Logic

#### Introduction

• Fuzzy Logic
• The Manual
• The Demonstration Notebooks
• The Packages
• Acknowledgments

#### New Features in This Release

• Introduction
• New Membership Functions
• Fuzzy Graph
• Defuzzifications
• 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

### 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

• 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