Fuzzy Logic

## Features

Membership Functions

• Triangular
• Trapezoidal
• Gaussian
• Bell-Shaped
• Double-Sided Gaussian
• Sigmoidal
• Digital
• User-Defined

Compositions and Inferencing

• Compositions--Max-Min, Max-Dot, Max-Star
• Rule-Based Inferencing for Multiple-Input/Single-Output Systems with Mamdani, Model, and Scaled Options
• Composition-Based Inferencing

Standard and Parameterized Fuzzy Aggregators

• Intersections and Unions--Min, Max, Hamacher, Frank, Yager, Dubois-Prade, Dombi, Yu, Weber
• Products and Sums--Drastic, Bounded, Algebraic, Einstein, Hamacher
• Means--Arithmetic, Geometric, Harmonic, Generalized
• User-Defined Aggregators

Fuzzy Operators

• Complements--Standard, Sugeno, Yager
• Defuzzifiers--Center of Area, Mean of Max, Smallest of Max, Largest of Max, Bisector of Area
• Normalization, Concentration, Dilation, Fuzzy Cardinality, Subsethood, Hamming Distance, Level Set, Alpha Cuts

Visualization of Fuzzy Sets and Relations

• Discrete, Line, and Crisp Plots of Fuzzy Sets
• Discrete 3D, Surface, and Wire-Frame Plots of Fuzzy Relations
• Fuzzy Graph
• Membership Matrices
• Defuzzification Results

Fuzzy System Modeling and Design Applications

Fuzzy Modeling

• System Definition
• Inferencing
• Model Building

Fuzzy Logic Control

• Fuzzy Inputs and Outputs
• Control Surfaces
• Linguistic Rules
• Animated Examples

Fuzzy Arithmetic

• Fuzzy Numbers
• Fuzzy Addition, Subtraction, Multiplication, and Division

Approximate Reasoning

• Linguistic Variables
• Hedges
• Modifiers
• Connectives

Lukasiewicz Sets and Logic

Fuzzy C-Means Clustering