pyfdm

Python 3 package with Fuzzy Decision Making (PyFDM) methods based on Triangular Fuzzy Numbers (TFN).

Version 1.2.0 adds 6 new MCDA methods, 6 subjective weighting methods, an expert-data collection and export module, group aggregation, step-by-step intermediate result inspection, and a standalone ranking utility — on top of a refactored, more robust core architecture. See What's new in 1.2.0 below.

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Table of contents

• Installation
• Local development setup
• Testing
• What's new in 1.2.0
• Modules and functionalities
• Usage examples
• Citations
• References

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Installation

The package can be installed from PyPI with pip:

pip install pyfdm

Excel-based features (FuzzyExporter.to_excel, StepLogger(output='excel')) require the optional openpyxl dependency. Install it together with the package using the excel extra:

pip install pyfdm[excel]

or separately:

pip install openpyxl

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Local development setup

To work on the library itself (contribute new methods, fix bugs, run the test suite against your changes), clone the repository and install it in editable mode.

1. Clone the repository

git clone https://github.com/jwieckowski/pyfdm.git
cd pyfdm

2. Create a virtual environment (recommended)

python3 -m venv .venv
source .venv/bin/activate        # Linux / macOS
.venv\Scripts\activate           # Windows

3. Install in editable mode with development dependencies

pip install -e ".[dev]"

This installs the package itself in editable mode (so source edits take effect immediately without reinstalling), plus pytest and openpyxl for running the full test suite, including Excel-export tests.

If you only need the core runtime dependencies without the dev extras:

pip install -e .

4. Verify the installation

python -c "import pyfdm; print(pyfdm.__file__)"

This should print a path inside your local repository clone, confirming the editable install is active.

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Testing

The test suite uses pytest and covers the core MCDA methods, validators, weighting methods, the expert/export module, group aggregation, sensitivity analysis, the step-by-step logger, and the standalone ranking utility.

Install test dependencies (if not already installed via pip install -e ".[dev]"):

pip install pytest openpyxl

Run the full suite from the repository root:

pytest tests

Run a specific test file:

pytest tests/test_methods.py -v
pytest tests/test_step_logger.py -v
pytest tests/test_ranking.py -v

Run with a short traceback (useful while developing):

pytest tests -v --tb=short

All tests are expected to pass with zero DeprecationWarnings on a clean checkout.

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What's new in 1.2.0

Architecture

• BaseFuzzyMethod — a shared abstract base class for all MCDA methods (pyfdm.methods.BaseFuzzyMethod). Eliminates duplicated rank() logic across 21 method classes and gives every method a consistent __repr__.
• StepLogger class (pyfdm.step_logger.StepLogger): captures every intermediate matrix and vector computed by an MCDA method or subjective weighting method. Activated by passing a StepLogger instance as logger= in any method's __init__. Supports console tables, JSON, CSV, and Excel output, individually or combined.
• intermediate_results now are included in both fuzzy MCDA methods and fuzzy subjective weighting methods. Can be used to verify and check partial results from the calculation process.
• Extended Validator — decision matrices, weights, and criteria types are now validated for shape, non-negativity, l <= m <= u TFN consistency, and absence of NaN/Inf, with descriptive error messages.
• Fixed validate_types bug — matrices where all criteria share the same type (all-profit or all-cost) are no longer incorrectly rejected.

New MCDA methods (6)

fAROMAN, fERVD, fMARCOS, fPIV, fRAFSI, fRIM — see the methods table below for details and references.

New subjective weighting methods (6)

fAHP, fBWM, fFUCOM, fLMAW, fRANCOM, fSWARA, available under pyfdm.weights.subjective. These complement the existing objective weighting methods (equal_weights, shannon_entropy_weights, standard_deviation_weights, variance_weights), which remain available from pyfdm.weights for backwards compatibility and are now also organised under pyfdm.weights.objective.

Expert data collection and export

pyfdm.expert.ExpertCollector collects integer ratings from multiple experts using a configurable linguistic scale (SCALE_1_5, SCALE_1_7, SCALE_1_9, or a custom scale) and converts them to TFN decision matrices. pyfdm.expert.FuzzyExporter exports collected data to CSV, JSON, or Excel.

Group aggregation

pyfdm.group.aggregate() combines TFN matrices from multiple experts using arithmetic mean, geometric mean, weighted average, or OWA (Ordered Weighted Average).

Intermediate-result inspection (logger)

Every MCDA method and subjective weighting method now accepts a logger= keyword argument in __init__. Pass a pyfdm.step_logger.StepLogger instance to capture every intermediate matrix and vector the method computes (normalized matrix, weighted matrix, distances, etc.) and render it as a console table, JSON file, CSV file, or Excel workbook — or any combination. See the usage example below.

Standalone ranking utility

pyfdm.utils.rank_alternatives() computes a ranking directly from any 1-D array of scores, independent of running an MCDA method, with five tie-breaking strategies (average, min, max, dense, ordinal) and full input validation. Useful for ranking externally computed scores (e.g. expert ratings, model outputs).

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Modules and functionalities

Fuzzy MCDA methods

Abbreviation	Full name	Reference
fARAS	fuzzy Additive Ratio ASsessment	[1]
fAROMAN	fuzzy Alternative Ranking Order Method Accounting for two-step Normalization	[33]
fCOCOSO	fuzzy Combined Compromise Solution	[32]
fCODAS	fuzzy COmbinative Distance-based ASsessment	[2]
fCOPRAS	fuzzy COmplex PRoportional ASsessment	[3]
fEDAS	fuzzy Evaluation based on Distance from Average Solution	[4]
fERVD	fuzzy Election based on Relative Value Distances	[34]
fMABAC	fuzzy Multi-Attributive Border Approximation area Comparison	[5]
fMAIRCA	fuzzy MultiAttributive Ideal-Real Comparative Analysis	[6]
fMARCOS	fuzzy Measurement of Alternatives and Ranking according to Compromise Solution	[35]
fMOORA	fuzzy Multi-Objective Optimization Method by Ratio Analysis	[7]
fOCRA	fuzzy Operational Competitiveness Ratings	[8]
fPIV	fuzzy Proximity Indexed Value	[36]
fRAFSI	fuzzy Ranking of Alternatives through Functional mapping of criterion Sub-Intervals into a Single Interval	[37]
fRIM	fuzzy Reference Ideal Method	[38]
fSPOTIS	fuzzy Stable Preference Ordering Towards Ideal Solution	[25]
fTOPSIS	fuzzy Technique for the Order of Prioritisation by Similarity to Ideal Solution	[9]
fVIKOR	fuzzy VIseKriterijumska Optimizacija I Kompromisno Resenje	[10]
fWASPAS	fuzzy Weighted Aggregated Sum Product Assessment	[26]
fWPM	fuzzy Weighted Product Model	[27]
fWSM	fuzzy Weighted Sum Model	[27]

Weighting methods — objective

Name	Reference
Equal weights	[11]
Shannon entropy weights	[12]
Standard deviation weights	[13]
Variance weights	[14]

Weighting methods — subjective

Abbreviation	Full name	Reference
fAHP	fuzzy Analytic Hierarchy Process	[39]
fBWM	fuzzy Best-Worst Method	[40]
fFUCOM	fuzzy Full Consistency Method	[41]
fLMAW	fuzzy Logarithm Methodology of Additive Weights	[42]
fRANCOM	fuzzy RANking COMparison	[43]
fSWARA	fuzzy Step-wise Weight Assessment Ratio Analysis.	[44]

Normalization methods

Name	Reference
COCOSO Normalization	[32]
Linear Normalization	[15]
Max Normalization	[2]
Min-Max Normalization	[5]
SAW Normalization	[3], [24]
Sum Normalization	[1]
Sqrt Normalization	[31]
Vector Normalization	[7]
WASPAS Normalization	[26]

Defuzzification methods

Name	Reference
Bisector defuzzification	[29]
Graded mean average defuzzification	[4]
Height defuzzification	[29]
Largest of Maximum defuzzification	[29]
Mean defuzzification	[16] [17]
Mean area defuzzification	[15]
Smallest of Maximum defuzzification	[29]
Weighted mean defuzzification	[10]

Distance measures

Name	Reference
Canberra distance	[30]
Chebyshev distance	[30]
Euclidean distance	[18]
Hamming distance	[19]
Mahdavi distance	[18]
L-R distance	[19]
Tran Duckstein distance	[19]
Vertex distance	[15]
Weighted Euclidean distance	[15]
Weighted Hamming distance	[15]

Correlation coefficients

Name	Reference
Pearson correlation coefficient	[21]
Spearman correlation coefficient	[20]
Weighted Spearman correlation coefficient	[22]
WS Rank Similarity coefficient	[23]

Triangular Fuzzy Number [28]

Functionality name
Addition
Subtractions
Multiplication
Division
Absolute value
Equality
Less equal comparison
Greater equal comparison
Round value
Membership function
Centroid
Core
Inclusion
S-norm operator
T-norm operator

Graphs

Functionality name
Multiple TFNs plot
Single TFN plot
S-norm operator plot
T-norm operator plot
TFN criteria plot
TFN membership plot

Helper / utility functions

Function	Module	Description
rank	pyfdm.utils	Legacy ranking helper (delegates to rank_alternatives).
rank_alternatives	pyfdm.utils	Standalone ranking from any score vector, with 5 tie-breaking strategies.
generate_fuzzy_matrix	pyfdm.utils	Generates a random TFN decision matrix.
normalize_weights	pyfdm.utils	Normalizes fuzzy criteria weights to [0, 1].
defuzzify_matrix	pyfdm.utils	Defuzzifies an entire TFN decision matrix.

Expert data collection and export

Component	Module	Description
ExpertCollector	pyfdm.expert	Collects per-expert integer ratings and converts them to TFN matrices.
FuzzyExporter	pyfdm.expert	Exports collected TFN data to CSV, JSON, or Excel.
SCALE_1_5, SCALE_1_7, SCALE_1_9	pyfdm.expert.scales	Built-in linguistic-to-TFN rating scales.

Group aggregation

Function	Module	Description
aggregate	pyfdm.group	Combines multiple expert TFN matrices ('geometric', 'arithmetic', 'weighted', 'owa').

Usage examples

More usage examples are available in Jupyter examples.

Basic MCDA ranking

from pyfdm.methods import fARAS
import numpy as np

matrix = np.array([
    [[5, 7, 9], [5, 7, 9], [7, 9, 9]],
    [[1, 3, 5], [3, 5, 7], [3, 5, 7]],
    [[1, 1, 3], [1, 3, 5], [1, 3, 5]],
    [[7, 9, 9], [7, 9, 9], [7, 9, 9]]
])

weights = np.array([[5, 7, 9], [7, 9, 9], [3, 5, 7]])
types = np.array([1, -1, 1])

f_aras = fARAS()
pref = f_aras(matrix, weights, types)

print(f'Fuzzy ARAS preferences: {pref}')
print(f'Fuzzy ARAS ranking: {f_aras.rank()}')

Output:

Fuzzy ARAS preferences: [1.011 0.854 1.312 0.993]
Fuzzy ARAS ranking: [2. 4. 1. 3.]

Inspecting intermediate computation steps

Every MCDA method accepts logger= to capture all intermediate matrices it computes (normalized matrix, weighted matrix, distances, etc.).

from pyfdm.methods import fMARCOS
from pyfdm.step_logger import StepLogger
import numpy as np

matrix = np.array([
    [[5, 7, 9], [5, 7, 9], [7, 9, 9]],
    [[1, 3, 5], [3, 5, 7], [3, 5, 7]],
    [[1, 1, 3], [1, 3, 5], [1, 3, 5]],
    [[7, 9, 9], [7, 9, 9], [7, 9, 9]]
], dtype=float)
weights = np.array([0.4, 0.35, 0.25])
types = np.array([1, -1, 1])

# Print to console
logger = StepLogger(output='console')
method = fMARCOS(logger=logger)
pref = method(matrix, weights, types)

# Or export to selected format
logger = StepLogger(output='json', path='results/marcos_steps')
method = fMARCOS(logger=logger)
pref = method(matrix, weights, types)
# -> results/marcos_steps.json,

Available output formats: 'console', 'json', 'csv', 'excel' (requires pip install pyfdm[excel]). Pass a single string or a list to combine formats.

Subjective weighting (fAHP)

from pyfdm.weights.subjective import fAHP
import numpy as np

# Pairwise TFN comparison matrix (criterion i vs criterion j)
comparison_matrix = np.array([
    [(1, 1, 1),       (2, 3, 4),       (4, 5, 6)],
    [(1/4, 1/3, 1/2), (1, 1, 1),       (2, 3, 4)],
    [(1/6, 1/5, 1/4), (1/4, 1/3, 1/2), (1, 1, 1)],
], dtype=float)

ahp = fAHP()
weights = ahp(comparison_matrix)   # shape (3, 3), TFN weights

Collecting expert judgements and exporting

from pyfdm.expert import ExpertCollector, FuzzyExporter
from pyfdm.expert.scales import SCALE_1_9

collector = ExpertCollector(n_alternatives=4, n_criteria=3, scale=SCALE_1_9)
collector.add_expert_matrix(0, [[9, 3, 7], [5, 9, 3], [3, 5, 9], [7, 3, 5]])
collector.add_expert_matrix(1, [[7, 5, 9], [9, 3, 5], [5, 7, 3], [3, 9, 7]])

exporter = FuzzyExporter(collector)
exporter.to_csv('expert_ratings.csv')
exporter.to_json('expert_ratings.json')
exporter.to_excel('expert_ratings.xlsx')   # requires openpyxl

Group aggregation of expert matrices

from pyfdm.group import aggregate

matrices = collector.get_tfn_matrices()           # list of (m, n, 3) arrays
agg_matrix = aggregate(matrices, method='geometric')

# or weighted by expert importance
agg_matrix = aggregate(matrices, method='weighted', weights=[0.6, 0.4])

Standalone ranking of external scores

Rank any 1-D array of scores directly, without running an MCDA method:

from pyfdm.methods import rank_alternatives

scores = [72.5, 88.0, 88.0, 60.1, 95.3]
ranking = rank_alternatives(scores, descending=True, method='average')
print(ranking)   # [3. 2.5 2.5 5. 1.]

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Citations

If you use pyFDM in your research to perform Fuzzy Multi-Criteria Decision Analysis (Fuzzy MCDA), please cite the appropriate publication corresponding to the version of the library used.

Initial version

APA:

Więckowski, J., Kizielewicz, B., & Sałabun, W. (2022). pyFDM: A Python library for uncertainty decision analysis methods. SoftwareX, 20, 101271.

https://doi.org/10.1016/j.softx.2022.101271

BibTeX:

@article{wikeckowski2022pyfdm,
  title={pyFDM: A Python library for uncertainty decision analysis methods},
  author={Wi{\k{e}}ckowski, Jakub and Kizielewicz, Bart{\l}omiej and Sa{\l}abun, Wojciech},
  journal={SoftwareX},
  volume={20},
  pages={101271},
  year={2022},
  publisher={Elsevier}
}

Version 1.1

APA:

Więckowski, J., & Sałabun, W. (2024). Version [1.1]-[pyFDM: A python library for uncertainty decision analysis methods]. SoftwareX, 25, 101607.

https://doi.org/10.1016/j.softx.2023.101607

BibTeX:

@article{wikeckowski2024version,
  title={Version [1.1]-[pyFDM: A python library for uncertainty decision analysis methods]},
  author={Wi{\k{e}}ckowski, Jakub and Sa{\l}abun, Wojciech},
  journal={SoftwareX},
  volume={25},
  pages={101607},
  year={2024},
  publisher={Elsevier}
}

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