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ADATSK

ADATSK extends TSK with an adaptive softmin antecedent that stabilizes high-dimensional fuzzy inference while preserving first-order TSK consequents.

Reference

G. Xue, Q. Chang, J. Wang, K. Zhang and N. R. Pal, "An Adaptive Neuro-Fuzzy System With Integrated Feature Selection and Rule Extraction for High-Dimensional Classification Problems," in IEEE Transactions on Fuzzy Systems, vol. 31, no. 7, pp. 2167-2181, July 2023, doi: 10.1109/TFUZZ.2022.3220950

Mathematical Formulation

ADATSK extends TSK fuzzy inference by using an adaptive softmin antecedent (Ada-softmin) together with first-order linear consequents.

Antecedent

Each rule-term membership is typically computed with a Gaussian function:

\[ \mu_{r,d}(x_d)=\exp\left(-\frac{(x_d-c_{r,d})^2}{2\sigma_{r,d}^2}\right) \]

where \(c_{r,d}\) is the center and \(\sigma_{r,d}>0\) is the spread.

In highFIS, the paper-strict ADATSKClassifier path uses a dedicated ADATSKGaussianMF antecedent, with:

\[ \mu(x)=\exp\left(-\frac{(x-c)^2}{\sigma^2}\right) \]

and applies sigma=1 before training, yielding the paper's simplified form:

\[ \mu(x)=\exp\left(-(x-c)^2\right) \]

Adaptive Ada-softmin aggregation

ADATSK computes rule firing strengths with an adaptive softmin based on the minimum antecedent membership for each rule:

\[ \hat{q}_r = \left\lceil \frac{690}{\ln (\min_{d}\mu_{r,d}(x_d))} \right\rceil, \quad \hat{q}_r \in [-1000, -1] \]
\[ \phi_r = \left( \frac{1}{D} \sum_{d=1}^{D}\mu_{r,d}(x_d)^{\hat{q}_r} \right)^{1/\hat{q}_r} \]

The exponent \(\hat{q}_r\) is recomputed on every forward pass and is clamped for numerical stability, which avoids the fixed-parameter softmin problems of underflow and fake minimum.

Normalization

Rule firing strengths are normalized by simple sum normalization:

\[ \bar{\phi}_r = \frac{\phi_r}{\sum_{k=1}^{R} \phi_k} \]

Consequent

In the ADATSK paper, the base formulation is presented for classification, with first-order TSK consequents:

\[ \mathbf{y}_r = W_r \mathbf{x} + \mathbf{b}_r \]

Output aggregation

The final prediction is the normalized weighted sum of rule consequents:

For classification:

\[ \mathbf{y} = \sum_{r=1}^{R} \bar{\phi}_r \mathbf{y}_r \]

Code ↔ Paper Correspondence

Equation Class / Method Description
Adaptive softmin highfis.layers.AdaSoftminRuleLayer Computes per-rule softmin exponents from the minimum membership value
Normalization highfis.defuzzifiers.SumBasedDefuzzifier Standard sum-based rule strength normalization
Consequent ClassificationConsequentLayer First-order linear consequents for classification
Membership functions highfis.memberships.ADATSKGaussianMF Paper-style Gaussian antecedent used by ADATSKClassifier

Implementation notes

In highFIS, ADATSKClassifierModel implements the paper-aligned ADATSK core by replacing the standard product antecedent with the adaptive softmin operator.

Model classes

  • ADATSKClassifierModel uses highfis.layers.AdaSoftminRuleLayer to compute rule strengths.
  • The classifier consequent remains first-order linear and is normalized with highfis.defuzzifiers.SumBasedDefuzzifier.
  • ADATSKClassifierModel does not expose the feature-selection/ rule-extraction gates of FSRE-ADATSK.

Estimator wrappers

  • ADATSKClassifier is the paper-strict default wrapper.
  • Default settings follow the paper protocol: n_mfs=3, mf_init="grid", rule_base="coco", full-batch updates (batch_size=None), and no shuffling.
  • For grid initialization, MF centers are placed directly on [V_{\min}, V_{\max}] with no margin padding.
  • In the pre-train hook, Gaussian spreads are set to sigma=1 and frozen.
  • Consequent parameters are initialized to zero in the ADATSK classifier paper-strict path.
  • For high-dimensional inputs (default threshold 1000 features), antecedent parameters are frozen by default to match the paper's experimental protocol.

Membership functions

  • The primary antecedent MFs are highfis.memberships.ADATSKGaussianMF objects in the paper-strict classifier path.
  • Gaussian spreads are fixed at sigma=1 in the paper-strict ADATSK path, reproducing Eq. (3).

Training in the paper vs. highFIS

  • The paper trains ADATSK end-to-end using full-batch gradient descent and MSE-style classification error.
  • The paper-strict ADATSK default in highFIS uses nn.MSELoss() for the classifier and SGD-based full-batch optimization.

  • eps is used to clamp membership values and stabilize log-space computations in AdaSoftminRuleLayer.

  • FSRE-ADATSK is documented separately in docs/models/fsre-adatsk.md.

Framework extensions (outside paper-strict scope)

  • ADATSKRegressorModel and ADATSKRegressor are provided as framework extensions for regression workflows.
  • highfis.memberships.CompositeGaussianMF remains available as an engineering alternative for custom experiments.

Alignment with the paper

  • The paper's key ADATSK contribution is the adaptive softmin antecedent operator to avoid numeric underflow and fake minimum effects.
  • highFIS implements this via AdaSoftminRuleLayer with a per-rule exponent derived from the rule's minimum antecedent membership.
  • The default ADATSKClassifier now follows the paper protocol (CoCo rule base, Eq. (3)-style Gaussian antecedent with sigma=1 fixed, full-batch GD, MSE-style classification loss, and zero-initialized consequents).
  • Regression and alternative MF variants are treated as explicit framework extensions, not part of the strict ADATSK paper baseline.