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Model Families

highFIS implements a diverse collection of concrete Takagi-Sugeno-Kang (TSK) neuro-fuzzy model architectures. These models are categorized below by their theoretical design, numerical stability properties, and structural sparsity capabilities.

Every model family exposes both a scikit-learn compatible Classifier (e.g., HTSKClassifier) and a Regressor (e.g., HTSKRegressor).

1. Baselines

These models implement standard, textbook fuzzy logic structures. They are ideal as simple baselines for low-dimensional problems.

  • TSK (Vanilla) — Standard TSK fuzzy system with product antecedent aggregation and sum-based normalization.

2. High-Dimensional & Stable Models

Standard fuzzy inference suffers from the saturation phenomenon in high-dimensional spaces (rule weights underflow or overflow). These models introduce mathematical formulations designed specifically to maintain numerical stability on large feature sets.

  • HTSK — High-dimensional TSK system featuring geometric mean aggregation and log-space softmax normalization.
  • LogTSK — Utilizes inverse-log normalization of log-domain rule weights to ensure stable inference under extreme dimensions.
  • HDFIS — Implements both high-dimensional product-DMF (HDFIS-prod) and minimum frozen-antecedent (HDFIS-min) inference.

3. Parametric & Adaptive T-Norms

These models replace static T-norms (like standard product or minimum) with parametric or adaptive aggregation functions whose shape parameters are trained via gradient descent.

  • DombiTSK — Parametric antecedent aggregation based on the Dombi T-norm with a learnable shape parameter \(\lambda\).
  • ADMTSK — Adaptive Dombi TSK utilizing dimension-dependent Gaussian membership functions.
  • AYATSK — Flexible antecedent aggregation utilizing the Yager T-norm.
  • ADATSK — Adaptive softmin aggregation offering dynamic rule weight scaling.
  • ADPTSK — Double-parameter adaptive softmin aggregation for enhanced weight stabilization.

4. Sparse & Gated Models (Interpretability)

These architectures embed structural gate parameters to perform feature selection (identifying key inputs) and rule extraction (identifying key decision paths) during the training phase.

  • FSRE-ADATSK — Features embedded feature selection and rule extraction gates in an adaptive softmin pipeline.
  • DGTSK — Double-gated TSK utilizing separate structural gates to prune features and rules.
  • DGALETSK — Combines double-gated pruning with adaptive Ln-Exp softmin aggregation.
  • MHTSK — Multihead subantecedents designed for sparse high-dimensional rule extraction.