Notes on Adaptive Neuro-Fuzzy Inference System (ANFIS)

Introduction

• Overview of the lecture on Adaptive Neuro-Fuzzy Inference System (ANFIS) and MATLAB implementation.
• Suggested to watch the previous video on fuzzy logic controllers for better understanding.

Neuro-Fuzzy Modeling

Fuzzy Logic Modeling

• Used when precise mathematical modeling is difficult due to system complexity.
• Incorporates human expertise through fuzzy rules and sets.
• Requires manual tuning, which is time-consuming and error-prone.

Neural Network-Based Modeling

• Utilizes artificial neural networks for system modeling.
• Effective when ample input-output data is available for training.
• Capable of learning but lacks fuzzy system's ability to manage uncertainty and represent human-like knowledge.

Combining Fuzzy and Neural Networks

• Neuro-Fuzzy Systems: Combine fuzzy systems with learning capabilities of neural networks.
• Benefits of both approaches are exploited through:
  • Cooperative Neuro-Fuzzy Systems
  • Concurrent Neuro-Fuzzy Systems
  • Hybrid Approaches

Adaptive Neuro-Fuzzy Inference System (ANFIS)

• Definition: A neuro-fuzzy system using a five-layer network with supervised learning.
• Proposed by Roger Jang and Sun in 1994.
• Architecture consists of five layers:
  1. Adaptive Layer: Contains membership functions (fuzzification).
  2. Fixed Layer: Performs multiplication of outputs from the first layer (firing strength).
  3. Normalization Layer: Normalizes firing strengths.
  4. Adaptive Layer: Updates consequent parameters based on training.
  5. Summation Layer: Outputs the final result.

Architecture Details

• Layer 1: Membership functions (Bell shape); outputs fuzzy values.
• Layer 2: Fixed nodes multiplying incoming signals.
• Layer 3: Normalizes outputs using defined equations.
• Layer 4: Adaptive layer that updates parameters governing the output functions.
• Layer 5: Summation of outputs from the previous layer.

Mathematical Operations Overview

• Fuzzification: Converts crisp input values into fuzzy values.
• Firing Strength Calculation: Operations in Layer 2 represent the fuzzy AND operation.
• Normalization: Achieved in Layer 3 to prepare for Layer 4 adjustments.

Hybrid Learning Algorithm

• Training Process: Involves updating both premise (input-side) and consequent (output-side) parameters using gradient descent and least squares estimates.

Applications of ANFIS

• Universal approximation for predictive modeling, time series prediction, controller design, pattern recognition, decision-making, etc.

MATLAB Implementation

Example of Universal Approximation

1. 1D Approximation (Sine Function)
   • Generate data for the sine function and utilize genfis to create the ANFIS model.
   • Train the model with specified parameters (number of membership functions, epochs).
   • Evaluate the model and compare outputs with actual sine wave.
   • Adjust parameters to see impacts on approximation accuracy.
2. 2D Approximation (Sinc Function)
   • Define input ranges, prepare data for training, and create the ANFIS model.
   • Train and evaluate the model, comparing the actual and estimated outputs.
   • Explore the effect of reducing membership functions and epochs on approximation quality.

Conclusion

• ANFIS acts as a universal approximator, capable of approximating any mathematical function by training with suitable parameters.
• The importance of choosing the right number of membership functions and epochs for better approximation is emphasized.