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Fuzzy Logic
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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

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