Nonsingular Gradient Descent Algorithm for Interval Type-2 Fuzzy Neural Network.

Area of Science:

• Artificial Intelligence
• Computational Intelligence
• Machine Learning

Background:

• Interval type-2 fuzzy neural networks (IT2FNNs) are effective for modeling nonlinear systems.
• Traditional gradient descent methods for IT2FNNs suffer from slow convergence due to inherent singularities.
• Uncertain variances in IT2FNNs can lead to convergence stagnation.

Purpose of the Study:

• To develop a novel nonsingular gradient descent algorithm (NSGDA) for updating IT2FNNs.
• To improve the convergence speed and stability of IT2FNNs in modeling nonlinear systems.
• To address the limitations of existing gradient descent algorithms in IT2FNN training.

Main Methods:

• Transformed the widths of type-2 fuzzy rules into root inverse variances (RIVs) to ensure differentiability.
• Reformulated singular RIVs using nonsingular Shapley-based matrices to avoid convergence stagnation.
• Developed an integrated-form update strategy (IUS) for efficient parameter updates, including RIVs, centers, and weights.
• Utilized parallel computation for parameter matrices to accelerate gradient convergence.

Main Results:

• The proposed NSGDA effectively overcomes the singularity issue in gradient descent for IT2FNNs.
• The RIV transformation and Shapley-based reformulation ensure sustained gradient convergence.
• The IUS accelerates parameter updates through parallel processing.
• Experimental results demonstrate a significant improvement in the convergence speed of the NSGDA-based IT2FNN.

Conclusions:

• The NSGDA provides a robust and efficient method for training IT2FNNs.
• This approach enhances the practical applicability of IT2FNNs for complex nonlinear system modeling.
• The study successfully addresses the convergence speed limitations of traditional IT2FNN training algorithms.