NeutroLab

A unified library for neutrosophic learning, configuration analysis, and logical machines.

NeutroLab is a comprehensive Python library for transforming crisp data into neutrosophic values using various data-driven and model-based methods. It implements the methods described in the paper:

"A Comparative Analysis of Data-Driven and Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic in Medical Data Transformation"

Overview

Neutrosophication is the process of converting crisp (deterministic) values into neutrosophic triplets (T, I, F), where:

• T (Truth): Degree of truth/membership
• I (Indeterminacy): Degree of indeterminacy/uncertainty
• F (Falsity): Degree of falsity/non-membership

Unlike fuzzy logic where T + F = 1, true neutrosophic logic allows T, I, and F to be independent, enabling more nuanced modeling of uncertainty.

Features

Current Implementation (v1.3.1)

• 5 Neutrosophication Methods: K-Means (proposed), Parabolic, Threshold, KDE, Fuzzy
• N-fsQCA v2.0: Neutrosophic Fuzzy-Set Qualitative Comparative Analysis
• NML: Neutrosophic Meta-Learning for Tsetlin Machines
• IFAO: Indeterminacy-First Aggregation Operator for MCDM
• True Neutrosophic Independence: K-Means method achieves independent T, I, F components
• Data-driven Adaptability: Methods automatically adapt to data distribution
• Consistent API: All methods follow the same interface (fit/transform)
• Comprehensive Statistics: Metrics from the paper (T+F consistency, entropy, etc.)

Planned Extensions

• 🔮 Interval-Valued Neutrosophic Sets (IVNS)
• 🔮 Neutrosophic Cognitive Maps
• 🔮 GPU acceleration for large-scale applications

Installation

pip install neutrolab

For development:

pip install neutrolab[dev]

For visualization:

pip install neutrolab[viz]

Quick Start

import numpy as np
from neutrolab import KMeansNeutrosophic, ParabolicNeutrosophic, normalize_data

# Sample data (e.g., clinical measurements)
raw_data = np.array([29, 45, 54, 62, 77])  # Age values

# Normalize to [0, 1] using Min-Max scaling (Eq. 1 from paper)
data = normalize_data(raw_data)

# Method 1: K-Means Clustering (PROPOSED - True Neutrosophic)
kmeans = KMeansNeutrosophic(random_state=42)
T, I, F = kmeans.fit_transform(data)

# K-Means achieves TRUE INDEPENDENCE: T+I+F ≠ 1
print(f"K-Means T+I+F sum: {np.mean(T + I + F):.3f}")  # ≈ 0.639

# Method 2: Parabolic (Classical - Fuzzy-like)
parabolic = ParabolicNeutrosophic(alpha=0.5)
T, I, F = parabolic.fit_transform(data)

# Parabolic enforces T+F=1 (fuzzy complementarity)
print(f"Parabolic T+I+F sum: {np.mean(T + I + F):.3f}")  # ≈ 1.331

Available Methods

1. K-Means Clustering (Proposed) ⭐

Data-driven approach achieving TRUE neutrosophic independence.

from neutrolab import KMeansNeutrosophic

method = KMeansNeutrosophic(random_state=42)
T, I, F = method.fit_transform(data)

Mathematical Formulation:

• T(x) = 1 / (1 + exp(-10·(x - c_high)/(σ_high + ε)))
• I(x) = 1 / (1 + |x - c_mid|/(σ_mid + ε))
• F(x) = 1 / (1 + exp(10·(x - c_low)/(σ_low + ε)))

Key Properties:

• ✅ TRUE independence of T, I, F (T+I+F ≈ 0.639)
• ✅ Data-driven: learns from data distribution
• ✅ High indeterminacy range (0.894)
• ✅ Moderate entropy (2.149)

2. Parabolic Method (Classical)

Parameter-free model-based approach.

from neutrolab import ParabolicNeutrosophic

method = ParabolicNeutrosophic(alpha=0.5)
T, I, F = method.fit_transform(data)

Mathematical Formulation:

• T(x) = x
• I(x) = 4·x·(1-x)·α
• F(x) = 1 - x

Best for: Speed-critical or real-time scenarios

3. Threshold Distance (Semi-novel)

Threshold-based approach with Gaussian indeterminacy.

from neutrolab import ThresholdNeutrosophic

method = ThresholdNeutrosophic(theta=0.5, lambda_=5.0)
T, I, F = method.fit_transform(data)

Mathematical Formulation:

• T(x) = 1 / (1 + exp(-10·(x - θ)))
• I(x) = exp(-λ·(x - θ)²)
• F(x) = 1 - T(x)

Best for: Threshold-based decision making

4. Kernel Density Estimation (KDE)

Density-based approach for anomaly detection.

from neutrolab import KDENeutrosophic

method = KDENeutrosophic(kernel='gaussian')
T, I, F = method.fit_transform(data)

Key Property: High indeterminacy in sparse regions (low density)

Best for: Anomaly detection and sparse region identification

5. Fuzzy Membership (Classical)

Triangular membership functions for interpretability.

from neutrolab import FuzzyNeutrosophic

method = FuzzyNeutrosophic()
T, I, F = method.fit_transform(data)

Predefined Fuzzy Sets:

• Low: (-0.5, 0.0, 0.5)
• Medium: (0.25, 0.5, 0.75)
• High: (0.5, 1.0, 1.5)

Best for: Interpretability-focused expert systems

Method Comparison

Method	T+I+F Sum	T+F Consistency	Independence	Best Use Case
K-Means	0.639	0.291	✅ TRUE	Complex data, true neutrosophic
Parabolic	1.331	1.000	❌ Forced	Real-time processing
Threshold	1.711	1.000	❌ Forced	Threshold decisions
KDE	1.260	1.000	❌ Forced	Anomaly detection
Fuzzy	1.349	1.000	❌ Forced	Expert systems

Comparing Methods

from neutrolab import (
    KMeansNeutrosophic, ParabolicNeutrosophic, 
    ThresholdNeutrosophic, KDENeutrosophic, FuzzyNeutrosophic,
    compare_methods, normalize_data
)
import numpy as np

# Prepare data
raw_data = np.random.random(100)
data = normalize_data(raw_data)

# Fit all methods
methods = {
    'K-Means': KMeansNeutrosophic(random_state=42),
    'Parabolic': ParabolicNeutrosophic(),
    'Threshold': ThresholdNeutrosophic(),
    'KDE': KDENeutrosophic(),
    'Fuzzy': FuzzyNeutrosophic()
}

results = {}
for name, method in methods.items():
    results[name] = method.fit_transform(data)

# Generate comparison table
comparison = compare_methods(results)
print(comparison[['Method', 'mean_sum', 'tf_consistency', 'entropy_I']])

N-fsQCA v2.0: Neutrosophic Qualitative Comparative Analysis

Enhanced validity in Qualitative Comparative Analysis through variance-based indeterminacy.

from neutrolab import NfsqcaEngine, compare_with_traditional
import pandas as pd

# Prepare fuzzy membership data [0,1]
X = pd.DataFrame({
    'Condition1': [0.8, 0.9, 0.2, 0.7],
    'Condition2': [0.7, 0.8, 0.3, 0.6]
})
y = pd.Series([0.9, 0.85, 0.1, 0.75])  # Outcome

# Run N-fsQCA v2.0
engine = NfsqcaEngine(threshold_t=0.80, threshold_i=0.30)
results = engine.analyze(X, y, use_bootstrap=True)

# Get sufficient configurations
sufficient = engine.get_sufficient_configurations()
for config in sufficient:
    print(f"{config.name}: T={config.tif.T:.3f}, I={config.tif.I:.3f}")

Key Innovation: Variance-Based Indeterminacy

I = Var(Y|X) / 0.25

11 Causal Archetypes:

• STRONG_SUFFICIENT, WEAK_SUFFICIENT, SUFFICIENT_CAUSE
• STRONG_INHIBITOR, WEAK_INHIBITOR, MEASUREMENT_ERROR
• CAUSAL_PARADOX, PARTIAL_CAUSE, IRRELEVANCE, COMPLEX_RELATION, INDETERMINATE

Validation Results:

• Jaccard similarity: 0.98 (vs 0.52 for traditional fsQCA)
• False positives: 0.03 (vs 1.85 for traditional fsQCA)

NML: Neutrosophic Tsetlin Machine

Post-hoc neutrosophic analysis for interpretable machine learning.

from neutrolab import NeutroTsetlinMachine, RuleCategory

# Prepare binary data
X_binary = NeutroTsetlinMachine.binarize(X_continuous)

# Train and analyze
ntm = NeutroTsetlinMachine(n_clauses=60, T=15, s=3.5)
ntm.fit(X_train, y_train, epochs=100)
ntm.analyze_neutrosophic(X_train, y_train)

# Get summary
summary = ntm.get_summary()
print(f"Active clauses: {summary['n_active']}")
print(f"T: {summary['T_mean']:.4f} ± {summary['T_std']:.4f}")
print(f"Certain rules: {summary['n_certain']}")

# Get specific rule categories
certain_rules = ntm.get_rules(RuleCategory.CERTAIN)

Rule Categories:

• CERTAIN: High certainty (I < 0.35)
• UNCERTAIN: High indeterminacy (I > 0.45)
• CONTRADICTORY: T ≈ F (|T - F| < 0.15)

Benefits:

• ~4% computational overhead
• Explicit uncertainty quantification
• Rule reliability classification

Note: Requires pyTsetlinMachine: pip install pyTsetlinMachine

Neutrosophic Aggregation: IFAO - Indeterminacy-First Aggregation Operator

A new paradigm for MCDM where Indeterminacy is the ontological foundation.

Formal Definition

The Indeterminacy-First Aggregation Operator (IFAO) is defined as:

Ω_IFAO: [0,1]ⁿ × Δⁿ → N₁

Ω_IFAO(v,w) = (P·(1-C), C, (1-P)·(1-C))

Where:

• v = (v₁, ..., vₙ) ∈ [0,1]ⁿ — criteria values
• w = (w₁, ..., wₙ) ∈ Δⁿ — weights (Σwᵢ = 1)
• N₁ = {(T,I,F) ∈ [0,1]³ : T+I+F = 1} — neutrosophic simplex

Mathematical Components

P = Σᵢ wᵢ·vᵢ                                    (Potential - WAM)
C = (2/n(n-1))·Σᵢ Σⱼ>ᵢ ((wᵢ+wⱼ)/2)·|vᵢ-vⱼ|    (Contradiction - Weighted GMD)
I = C                                           (Indeterminacy = Conflict)
T = P·(1-I)                                     (Truth - derived from I)
F = (1-P)·(1-I)                                 (Falsity - derived from I)

Fundamental Property: T + I + F = 1

Ontological Hierarchy

IFAO:       Conflict → Indeterminacy → (Truth, Falsity)  [I is PRIMARY]
Atanassov:  Truth, Falsity → Indeterminacy = 1-T-F       [I is RESIDUAL]

Cross-Domain Analogies

The IFAO follows a deep epistemological pattern found in:

Domain	Primary	Derived	Constraint
Quantum Mechanics	Uncertainty (ℏ)	Position, Momentum	Δx·Δp ≥ ℏ/2
Thermodynamics	Entropy (S)	Useful Work	η = 1-Tc/Th
Finance (Markowitz)	Risk (σ)	Adjusted Return	Efficient Frontier
IFAO	Indeterminacy (C)	Truth, Falsity	T+I+F=1

Usage Example

from neutrolab import IndeterminacyFirstAggregator, MCDMEvaluator

# Define criteria and weights
criteria = ['Technical', 'Financial', 'Social', 'Environmental']
weights = [0.3, 0.3, 0.2, 0.2]
agg = IndeterminacyFirstAggregator(criteria, weights)

# Harmonious project - low conflict
result = agg.aggregate([0.8, 0.8, 0.7, 0.75])
print(f"⟨T={result.T:.3f}, I={result.I:.3f}, F={result.F:.3f}⟩")
# Output: ⟨T=0.754, I=0.014, F=0.232⟩ → STRONG_APPROVE

# Conflicting project - high conflict
result = agg.aggregate([0.9, 0.2, 0.8, 0.1])
print(f"⟨T={result.T:.3f}, I={result.I:.3f}, F={result.F:.3f}⟩")
# Output: ⟨T=0.481, I=0.125, F=0.394⟩ → REVIEW (conflicted, not mediocre!)

# Batch evaluation
evaluator = MCDMEvaluator(criteria, weights)
alternatives = {
    'Project A': [0.8, 0.8, 0.7, 0.75],
    'Project B': [0.9, 0.2, 0.8, 0.1],
    'Project C': [0.4, 0.3, 0.5, 0.35]
}
results = evaluator.evaluate_all(alternatives)
ranking = evaluator.rank_alternatives(results, method='truth_adjusted')

Decision Categories:

• STRONG_APPROVE: High T, Low I
• APPROVE: Moderate T, Low I
• REVIEW_POSITIVE: High T, Moderate I
• REVIEW_NEGATIVE: Low T, Moderate I
• REJECT: Low T, Low I
• INDETERMINATE: Very High I

Requirements

• Python >= 3.8
• NumPy >= 1.20.0
• Pandas >= 1.3.0
• SciPy >= 1.7.0

Citation

If you use NeutroLab in your research, please cite:

@article{leyvavazquez2024neutrosophication,
  title={A Comparative Analysis of Data-Driven and Model-Based Neutrosophication 
         Methods: Advancing True Neutrosophic Logic in Medical Data Transformation},
  author={Leyva-V{\'a}zquez, Maikel Yelandi and Smarandache, Florentin},
  journal={},
  year={2024}
}

Authors

• Maikel Yelandi Leyva-Vázquez - Universidad de Guayaquil, Ecuador
  • Email: mleyvaz@gmail.com
  • ORCID: 0000-0001-7911-5879
• Florentin Smarandache - University of New Mexico, USA
  • ORCID: 0000-0002-5560-5926

References

1. Smarandache, F. (1998). Neutrosophy/neutrosophic probability, set, and logic.
2. Smarandache, F. (2014). Introduction to Neutrosophic Statistics.
3. Wang, H., et al. (2010). Single valued neutrosophic sets.
4. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request