Fuzzy Modeling of Asphalt Mechanical Properties

This project implements a complete Takagi–Sugeno–Kang (TSK) fuzzy inference system using the Wang–Mendel rule generation method to model mechanical properties of asphalt mixtures.

The system is implemented from scratch using:

• NumPy

• Pandas

• Matplotlib

No external fuzzy logic libraries were used.

Objectives

• Model nonlinear relationships between asphalt mixture parameters and mechanical properties.

• Compare system performance using different numbers of fuzzy partitions.

• Analyze rule growth and complexity.

• Evaluate prediction quality using RMSE.

• Visualize model interpretability and error behavior.

📂 Project Structure

  ctx3 print <- this tool is mine! check it's repo!
┌── 📂 Project structure:
├── .gitignore (4699 bytes)
├── README.md (5386 bytes)
├── data (96 bytes)
│   └── Asphalt-Dataset-ToClass.xlsx (32029 bytes)
├── plots (672 bytes) (Generated plots reside here!)
|
├── report (64 bytes)
└── src (352 bytes)
    ├── data_loader.py (947 bytes)
    ├── evaluation.py (257 bytes)
    ├── fuzzy_sets.py (1029 bytes)
    ├── preprocessing.py (692 bytes)
    ├── training.py (900 bytes)
    ├── tsk_model.py (1535 bytes)
    ├── visualize.py (3399 bytes)
    └── wang_mendel.py (1599 bytes)
 ├── main.py (1886 bytes)

You can use ctx3 (context tree) to quickly grasp the structure. click here to install ctx3

Methodology

The system follows the classical fuzzy modeling framework:

Data Preprocessing

• 80% training / 20% testing split

• Random shuffling with fixed seed

• Min–Max normalization (training statistics only)

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Fuzzy Partitioning

Each input variable is partitioned into:

• 2 fuzzy sets

• 3 fuzzy sets

• 4 fuzzy sets

Uniform triangular membership functions are used.

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Rule Generation (Wang–Mendel)

For each training sample:

1. Select maximum membership per input

2. Construct fuzzy rule

3. Assign rule weight

4. Remove duplicates (keep strongest)

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TSK Inference

Zero-order TSK model:

$y = \frac{\sum w_k c_k}{\sum w_k}$

Where:

• ( $w_k$ ) = firing strength

• ( $c_k$ ) = rule consequent

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Evaluation

Metric used:

$RMSE = \sqrt{\frac{1}{N} \sum (y_{true} - y_{pred})^2}$

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Outputs Generated

After running the project, the following plots are saved inside /plots:

For each of the 4 outputs:

• RMSE vs number of fuzzy sets

• Rule count vs number of fuzzy sets

• True vs predicted scatter

• Residual distribution

Additionally:

• Membership function visualizations (selected inputs)

Total: ~19 plots.

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How to Run

Option 1 — Using uv (Recommended)

If you use uv:

Step 1 — Install dependencies

uv add numpy pandas matplotlib openpyxl

(If already installed, skip this step.)

Step 2 — Run the project

uv run main.py

All plots will be saved automatically inside:

./plots

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Option 2 — Without uv (Standard Python)

Step 1 — Create virtual environment (optional but recommended)

python -m venv venv

Activate it:

Mac/Linux

source venv/bin/activate

Windows

venv\Scripts\activate

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Step 2 — Install dependencies

pip install numpy pandas matplotlib openpyxl

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Step 3 — Run

python main.py

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Required Dependencies

• Python 3.9+

• numpy

• pandas

• matplotlib

• openpyxl

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Experimental Results Summary

Rule Growth

Rule count increases with partition granularity.

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Performance Trend

Best performance was achieved using:

2 fuzzy sets per input

Increasing the number of partitions:

• Increased rule count

• Increased model complexity

• Led to mild overfitting

This demonstrates the classical bias–variance tradeoff.

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Key Observations

• ITSM outputs were predicted more accurately than Flow.

• Increasing fuzzy granularity without increasing dataset size leads to sparse rule regions.

• Proper data splitting and normalization were critical to avoid data leakage.

• Results align with theoretical expectations from fuzzy system theory.

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Conclusion

This project successfully demonstrates:

• End-to-end fuzzy modeling

• Wang–Mendel rule extraction

• TSK inference

• Complexity vs performance tradeoff

• Interpretability through rule and membership visualization

The implementation is mathematically consistent and academically defensible.

License

Academic project implementation.