pyfuzzy-toolbox Quick Start Guides¶

Complete collection of quick start guides for all modules in the pyfuzzy-toolbox library.

📚 Available Guides¶

🎛️ Fuzzy Inference Systems¶

Build and use fuzzy inference systems for control and decision-making.

1. Mamdani System ¶

Linguistic fuzzy inference with fuzzy outputs

✅ Manual or automatic membership function generation
✅ Intuitive rule creation (dictionaries, lists, indices)
✅ Multiple defuzzification methods
📓 Notebooks: 02_inference/01_mamdani_tipping.ipynb, 02_inference/02_voting_prediction.ipynb

Key Features: - add_auto_mfs(): automatic MF generation with linguistic labels - Multiple rule formats: dict, list, tuple - Visualization: plot_variables(), plot_output(), plot_rule_matrix() - Save/load: save(), load(), export_rules(), import_rules()

When to use: Human-interpretable control systems, linguistic rules, fuzzy decision-making.

2. Sugeno System ¶

Efficient fuzzy inference with mathematical consequents

✅ Order 0 (constant) or Order 1 (linear) consequents
✅ No defuzzification needed (weighted average)
✅ Ideal for ANFIS and optimization
📓 Notebooks: 02_inference/03_sugeno_zero_order.ipynb, 02_inference/04_sugeno_first_order.ipynb

Key Features: - Order 0: IF-THEN rules with constant outputs (singletons) - Order 1: IF-THEN rules with linear functions of inputs - Faster computation than Mamdani - Better for learning algorithms (ANFIS compatible)

When to use: Optimization tasks, ANFIS learning, smooth approximations, computational efficiency.

🧠 Learning Algorithms¶

Learn fuzzy systems from data using various learning techniques.

3. Wang-Mendel Learning ¶

Single-pass fuzzy rule extraction from data

✅ Fast rule generation from training data
✅ Automatic task detection (regression/classification)
✅ No iterative optimization needed
📓 Notebooks: 03_learning/wang_mendel_nonlinear.ipynb, 03_learning/wang_mendel_iris.ipynb

Key Features: - One-pass algorithm (very fast) - Automatic membership function generation - Rule conflict resolution - Handles multi-output systems

When to use: Quick fuzzy model from data, interpretable rules, baseline models.

4. ANFIS - Adaptive Neuro-Fuzzy Inference System ¶

Hybrid learning combining neural networks and fuzzy logic

✅ Supervised learning for regression/classification
✅ Two training methods: fit() (gradient descent) and fit_metaheuristic() (PSO/DE/GA)
✅ Automatic parameter optimization
📓 Notebooks: 03_learning/anfis_regression.ipynb, 03_learning/anfis_iris.ipynb

Key Features: - Gaussian, Bell, and Sigmoid membership functions - Hybrid learning: LSE for consequents + gradient descent for premises - Metaheuristic optimization: PSO, DE, GA - Early stopping and adaptive learning rate

When to use: Complex nonlinear regression/classification with automatic rule extraction.

5. Mamdani Learning ¶

Optimize Mamdani fuzzy system consequents with metaheuristics

✅ Optimize rule consequents for existing Mamdani FIS
✅ Four metaheuristic algorithms: SA, GA, PSO, DE
✅ Preserves linguistic interpretability
📓 Notebooks: 03_learning/rules_optimization.ipynb, 03_learning/rules_optimization_iris.ipynb

Key Features: - Simulated Annealing (SA): local search with probabilistic acceptance - Genetic Algorithm (GA): population-based with crossover/mutation - Particle Swarm Optimization (PSO): swarm intelligence - Differential Evolution (DE): mutation-based evolution

When to use: Fine-tune existing Mamdani systems, optimize rule consequents while keeping antecedents.

🔄 Dynamical Systems¶

Model temporal evolution with fuzzy rules.

6. p-Fuzzy Discrete ¶

Discrete-time fuzzy dynamical systems

✅ Model discrete-time evolution: x_{n+1} = x_n + f(x_n)
✅ Absolute or relative modes
✅ Single-step execution for analysis
📓 Notebooks: 04_dynamics/pfuzzy_discrete_predator_prey.ipynb, 04_dynamics/pfuzzy_population.ipynb

Key Features: - Absolute mode: x_{n+1} = x_n + f(x_n) (additive change) - Relative mode: x_{n+1} = x_n × f(x_n) (multiplicative change) - simulate(): run n_steps iterations - step(): single iteration for manual control - Export: to_csv() with international/Brazilian formats

When to use: Population dynamics (generations), discrete events, time-series with discrete steps.

7. p-Fuzzy Continuous ¶

Continuous-time fuzzy dynamical systems with ODEs

✅ Model continuous evolution: dx/dt = f(x)
✅ Euler or RK4 integration methods
✅ Fixed or adaptive time stepping
📓 Notebooks: 04_dynamics/pfuzzy_continuous_predator_prey.ipynb

Key Features: - Absolute mode: dx/dt = f(x) (rate independent of state) - Relative mode: dx/dt = x·f(x) (rate proportional to state) - Integration methods: 'euler' (fast), 'rk4' (accurate) - Adaptive stepping: automatically adjusts dt for accuracy - Verbose mode: prints statistics (accepted/rejected steps, dt range)

When to use: Physical processes, continuous growth, temperature/cooling systems, smooth dynamics.

8. Fuzzy ODE Solver ¶

Solve ODEs with fuzzy initial conditions and parameters

✅ Propagate uncertainty through differential equations
✅ Fuzzy numbers for initial conditions and parameters
✅ Three solution methods: standard, Monte Carlo, hierarchical
📓 Notebooks: 04_dynamics/fuzzy_ode_logistic.ipynb, 04_dynamics/fuzzy_ode_holling_tanner.ipynb

Key Features: - Fuzzy numbers: triangular, gaussian, trapezoidal - α-cuts: confidence levels for uncertainty quantification - Solution methods: - 'standard': full grid (most accurate) - 'monte_carlo': sampling (10-400x faster for high dimensions) - 'hierarchical': optimization (3-5x faster) - Visualization: plot α-level envelopes - Export: to_csv(), to_dataframe()

When to use: Uncertain initial conditions, imprecise parameters, possibilistic uncertainty (vs probabilistic).

🗂️ Quick Reference Table¶

Module	Type	Input	Output	Best For	Guide
Mamdani System	Inference	Variables + Rules	FIS	Linguistic control	Guide
Sugeno System	Inference	Variables + Rules	FIS	Efficient inference	Guide
Wang-Mendel	Learning	Data (X, y)	Mamdani FIS	Fast rule extraction	Guide
ANFIS	Learning	Data (X, y)	Sugeno FIS	Regression, classification	Guide
Mamdani Learning	Learning	FIS + Data	Optimized FIS	Fine-tuning consequents	Guide
p-Fuzzy Discrete	Dynamics	FIS + x₀	Trajectory	Discrete-time evolution	Guide
p-Fuzzy Continuous	Dynamics	FIS + x₀	Trajectory	Continuous-time evolution	Guide
Fuzzy ODE	Dynamics	ODE + Fuzzy params	Fuzzy trajectory	Uncertainty propagation	Guide

📂 Notebook Organization¶

All notebooks are available in the notebooks_colab/ directory:

notebooks_colab/
├── 01_fundamentals/          # Fuzzy logic basics
│   ├── 01_membership_functions.ipynb
│   ├── 02_fuzzy_operations.ipynb
│   ├── 03_linguistic_variables.ipynb
│   └── 04_fuzzy_relations.ipynb
│
├── 02_inference/              # Inference systems
│   ├── 01_mamdani_tipping.ipynb
│   ├── 02_sugeno_zero_order.ipynb
│   ├── 03_sugeno_first_order.ipynb
│   └── 04_voting_prediction.ipynb
│
├── 03_learning/               # Learning algorithms
│   ├── 01_anfis_regression.ipynb
│   ├── 02_anfis_classification.ipynb
│   ├── 03_wang_mendel_regression.ipynb
│   ├── 04_wang_mendel_classification.ipynb
│   └── 05_mamdani_learning_optimization.ipynb
│
└── 04_dynamics/               # Dynamical systems
    ├── 01_pfuzzy_discrete_predator_prey.ipynb
    ├── 02_pfuzzy_continuous_predator_prey.ipynb
    ├── 03_pfuzzy_discrete_population.ipynb
    ├── 04_fuzzy_ode_logistic.ipynb
    └── 05_fuzzy_ode_holling_tanner.ipynb

🚀 Getting Started¶

Installation¶

pip install pyfuzzy-toolbox

Choose Your Path¶

1️⃣ I want to build a control system¶

→ Start with Mamdani System for interpretability, or Sugeno System for efficiency

2️⃣ I want to learn from data¶

→ Start with Wang-Mendel for quick rules, or ANFIS for accurate models

3️⃣ I want to model temporal dynamics¶

→ Start with p-Fuzzy Discrete for discrete-time, or p-Fuzzy Continuous for continuous-time

4️⃣ I have uncertain parameters¶

→ Start with Fuzzy ODE Solver

📖 Learning Path¶

Beginner Path¶

Fundamentals → Notebooks 01_fundamentals/
Inference → Mamdani System
Learning → Wang-Mendel

Intermediate Path¶

Advanced Inference → Sugeno System
Learning → ANFIS
Dynamics → p-Fuzzy Discrete

Advanced Path¶

Optimization → Mamdani Learning
Continuous Dynamics → p-Fuzzy Continuous
Uncertainty → Fuzzy ODE Solver

💡 Common Use Cases¶

Control Systems¶

Tipping problem: Mamdani System → Notebook 02_inference/01_mamdani_tipping.ipynb
Temperature control: Sugeno System → Notebook 02_inference/03_sugeno_zero_order.ipynb

Machine Learning¶

Regression: ANFIS → Notebook 03_learning/anfis_regression.ipynb
Classification: Wang-Mendel → Notebook 03_learning/wang_mendel_iris.ipynb

Population Dynamics¶

Predator-prey (discrete): p-Fuzzy Discrete → Notebook 04_dynamics/pfuzzy_discrete_predator_prey.ipynb
Predator-prey (continuous): p-Fuzzy Continuous → Notebook 04_dynamics/pfuzzy_continuous_predator_prey.ipynb

Uncertainty Modeling¶

Logistic growth with fuzzy parameters: Fuzzy ODE Solver → Notebook 04_dynamics/fuzzy_ode_logistic.ipynb
Epidemic model with uncertain transmission: Fuzzy ODE Solver → Notebook 04_dynamics/fuzzy_ode_holling_tanner.ipynb

🔗 Additional Resources¶

Main Documentation: https://1moi6.github.io/pyfuzzy-toolbox/
GitHub Repository: https://github.com/1moi6/pyfuzzy-toolbox
PyPI Package: https://pypi.org/project/pyfuzzy-toolbox/
Issue Tracker: https://github.com/1moi6/pyfuzzy-toolbox/issues

📝 Document Structure¶

Each quickstart guide follows the same structure:

Overview - What is it and why use it
Basic Concepts - Key ideas and terminology
Getting Started - Minimal working example
Parameters - Detailed parameter descriptions
Methods - Available methods and their uses
Visualization - How to plot results
Export - Saving results
Complete Examples - Real-world applications
Tips & Best Practices - Expert recommendations
Common Issues - Troubleshooting guide
Advanced Features - Power-user techniques
References - Academic citations

Inference: Mamdani System | Sugeno System
Learning: Wang-Mendel | ANFIS | Mamdani Learning
Dynamics: p-Fuzzy Discrete | p-Fuzzy Continuous | Fuzzy ODE

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