ADMTSK and DombiTSK

Article: G. Xue, L. Hu, J. Wang and S. Ablameyko, "ADMTSK: a high-dimensional Takagi-Sugeno-Kang fuzzy system based on adaptive Dombi T-norm", IEEE Transactions on Fuzzy Systems, vol. 33, no. 6, 2025.

Script: examples/reproductions/admtsk_2025.py

Protocol of the Article

Section IV-A of the article. Except for the learning rate and the batch size, which the script varies as the article does, these settings are the defaults of ADMTSKClassifier.

Point	Article	In the script
Inputs	scaled to \([0, 1]\)	`MinMaxScaler` fitted on the training part
Fuzzy sets	three per feature, centres 0, 0.5 and 1, spreads of 1	defaults (`mf_init="grid"`, `n_mfs=3`)
Membership	composite Gaussian, bounded below by \(1/e\) (Eq. 31)	default (`GaussianPiMF`)
T-norm	Dombi with \(\lambda = \ln D / (\ln(K - \varepsilon) - \ln(1 - \varepsilon))\), \(K = 10\)	default (`adaptive=True`, `k=10`)
Consequents	start at zero	default
Optimizer	Adam, 50 epochs, batches of 10% or 20% of the training samples	default (`epochs=50`); both batch sizes
Learning rate	0.01, 0.001 or 0.0001; the best of the six combinations with the batch size is reported	the three values; the six combinations are printed, and the best
Evaluation	ten-fold cross-validation, repeated five times	the same, stratified folds

Result

Output of the script, on four threads; the standard deviation is over the 50 runs:

ADMTSK: mean test accuracy in percent of each combination
dataset   learning rate  batch  highFIS    std
Colon              0.01    10%    85.86  12.68
Colon              0.01    20%    84.86  11.49
Colon             0.001    10%    82.86  11.45
Colon             0.001    20%    82.86   9.89
Colon            0.0001    10%    87.57  10.79
Colon            0.0001    20%    86.24  11.22
Leukemia           0.01    10%    97.43   5.49
Leukemia           0.01    20%    97.43   5.49
Leukemia          0.001    10%    97.14   5.71
Leukemia          0.001    20%    96.86   5.92
Leukemia         0.0001    10%    96.86   5.92
Leukemia         0.0001    20%    97.14   5.71

Table V: the best of the six combinations (mean test accuracy in percent)
dataset    article  highFIS
Colon        86.33    87.57
Leukemia     97.29    97.43

Summary of the last model fitted
ADMTSKClassifier
  task               classification, 2 classes
  features           7129 seen in fit, 7129 used by the model
  rules              3 (rule base: coco)
  fuzzy sets         3 per feature, GaussianPiMF
  firing strength    RuleLayer, T-norm AdaptiveDombiTNorm
  defuzzifier        SumBasedDefuzzifier
  consequents        ClassificationConsequentLayer
  parameters         85554 trainable (42774 antecedent, 42780 consequent)
Training
  batch size         13
  epochs             50 epochs, learning rate 0.0001, training loss 0.3134 -> 0.0044, training accuracy 1.0000

The best of the six combinations is within 1.3 points of the article on Colon and within 0.2 point on Leukemia.

The Six Combinations

The article reports, for each dataset, the best of the six combinations, and the last table of the output does the same. The defaults of ADMTSKClassifier on these datasets are the third combination: a learning rate of 0.001 above 1000 features and batches of 10%. For your own data, choose the combination on a validation part of the training data.

On SRBCT (83 samples, 2308 genes), with ten folds, the best of the six combinations is 98.89, against 98.81 in the article.

Differences from the Article

Loss. The article minimizes the squared error on one-hot targets summed over the classes and halved (Eq. 9); highFIS uses the mean squared error, which differs by a constant factor that Adam compensates.
DombiTSK. In the article DombiTSK is the same system with a fixed \(\lambda\) and is evaluated with the same partition. DombiTSKClassifier defaults to clustering with five rules and 100 epochs, a choice for general use; pass mf_init="grid", n_mfs=3, rule_base="coco", epochs=50 for the setting of the article.
Datasets. The article uses sixteen datasets. Colon and Leukemia are the two that OpenML provides with the samples and features of the article and without further dependencies; SRBCT above uses the copy distributed with the code of the HDFIS article.

Reproducibility

The script fixes the seeds, uses deterministic algorithms and four threads, and ends by printing the versions of the libraries and the processor. Another number of threads, another processor or another version of the numerical libraries can change the result.

Run It

python examples/reproductions/admtsk_2025.py

The data are downloaded from OpenML on the first run. A run takes several hours, most of them on Leukemia; remove it from DATASETS in the script for a run of about half an hour.