Generalized neurofuzzy network modeling algorithms using Bézier-Bernstein polynomial functions and additive...

Area of Science:

• Computational intelligence
• Neurofuzzy systems
• Nonlinear dynamic systems

Background:

• Traditional fuzzy and radial basis function (RBF) networks struggle with the curse of dimensionality in high-dimensional systems.
• Existing neurofuzzy systems often lack structural parsimony and interpretability.

Purpose of the Study:

• Introduce a new neurofuzzy model construction algorithm for nonlinear dynamic systems.
• Address the curse of dimensionality in n-dimensional input systems.
• Leverage Bézier-Bernstein polynomial functions for enhanced model properties.

Main Methods:

• Utilized an additive decomposition construction for n-dimensional inputs.
• Incorporated univariate and bivariate Bézier-Bernstein polynomial functions.
• Employed conventional least squares methods for network weight learning.

Main Results:

• Demonstrated effectiveness in modeling nonlinear dynamic systems through numerical examples.
• Achieved structural parsimony and Delaunay input space partition.
• Overcame the curse of dimensionality inherent in conventional fuzzy and RBF networks.

Conclusions:

• The proposed Bézier-Bernstein polynomial-based neurofuzzy network offers a powerful and interpretable approach for modeling complex systems.
• The additive decomposition and specific basis function choices effectively manage high-dimensional data.
• This data-based modeling approach shows significant promise for practical applications.