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PyMCDM

Python 3 library for solving multi-criteria decision-making (MCDM) problems.

Documentation is avaliable on readthedocs.


Installation

You can download and install pymcdm library using pip:

pip install pymcdm

You can run all tests with following command from the root of the project:

python -m unittest -v

Citing pymcdm

If usage of the pymcdm library lead to a scientific publication, please acknowledge this fact by citing "Kizielewicz, B., Shekhovtsov, A., & Sałabun, W. (2023). pymcdm—The universal library for solving multi-criteria decision-making problems. SoftwareX, 22, 101368."

Or using BibTex:

@article{kizielewicz2023pymcdm,
  title={pymcdm—The universal library for solving multi-criteria decision-making problems},
  author={Kizielewicz, Bart{\l}omiej and Shekhovtsov, Andrii and Sa{\l}abun, Wojciech},
  journal={SoftwareX},
  volume={22},
  pages={101368},
  year={2023},
  publisher={Elsevier}
}

DOI: https://doi.org/10.1016/j.softx.2023.101368


Available methods

The library contains:

  • MCDA methods:
Acronym Method Name Reference
TOPSIS Technique for the Order of Prioritisation by Similarity to Ideal Solution [1]
VIKOR VIseKriterijumska Optimizacija I Kompromisno Resenje [2]
COPRAS COmplex PRoportional ASsessment [3]
PROMETHEE I & II Preference Ranking Organization METHod for Enrichment of Evaluations I & II [4]
COMET Characteristic Objects Method [5]
SPOTIS Stable Preference Ordering Towards Ideal Solution [6]
ARAS Additive Ratio ASsessment [7],[8]
COCOSO COmbined COmpromise SOlution [9]
CODAS COmbinative Distance-based ASsessment [10]
EDAS Evaluation based on Distance from Average Solution [11],[12]
MABAC Multi-Attributive Border Approximation area Comparison [13]
MAIRCA MultiAttributive Ideal-Real Comparative Analysis [14],[15],[16]
MARCOS Measurement Alternatives and Ranking according to COmpromise Solution [17],[18]
OCRA Operational Competitiveness Ratings [19],[20]
MOORA Multi-Objective Optimization Method by Ratio Analysis [21],[22]
RIM Reference Ideal Method [48]
ERVD Election Based on relative Value Distances [49]
PROBID Preference Ranking On the Basis of Ideal-average Distance [50]
WSM Weighted Sum Model [51]
WPM Weighted Product Model [52]
WASPAS Weighted Aggregated Sum Product ASSessment [53]
  • Weighting methods:
Acronym Method Name Reference
- Equal/Mean weights [23]
- Entropy weights [23],[24],[25]
STD Standard Deviation weights [23],[26]
MEREC MEthod based on the Removal Effects of Criteria [27]
CRITIC CRiteria Importance Through Intercriteria Correlation [28],[29]
CILOS Criterion Impact LOS [30]
IDOCRIW Integrated Determination of Objective CRIteria Weight [30]
- Angular/Angle weights [31]
- Gini Coeficient weights [32]
- Statistical variance weights [33]
  • Normalization methods:
Method Name Reference
Weitendorf’s Linear Normalization [34]
Maximum - Linear Normalization [35]
Sum-Based Linear Normalization [36]
Vector Normalization [36],[37]
Logarithmic Normalization [36],[37]
Linear Normalization (Max-Min) [34],[38]
Non-linear Normalization (Max-Min) [39]
Enhanced Accuracy Normalization [40]
Lai and Hwang Normalization [38]
Zavadskas and Turskis Normalization [38]
  • Correlation coefficients:
Coefficient name Reference
Spearman's rank correlation coefficient [41],[42]
Pearson correlation coefficient [43]
Weighted Spearman’s rank correlation coefficient [44]
Rank Similarity Coefficient [45]
Kendall rank correlation coefficient [46]
Goodman and Kruskal's gamma [47]
Drastic Weighted Similarity (draWS) In Press
Weights Similarity Coefficient (WSC) In Press
Weights Similarity Coefficient 2 (WSC2) In Press
  • Helpers
Helpers submodule Description
rankdata Create ranking vector from the preference vector. Smaller preference values has higher positions in the ranking.
rrankdata Alias to the rankdata which reverse the sorting order.
correlation_matrix Create the correlation matrix for given coefficient from several the several rankings.
normalize_matrix Normalize decision matrix column by column using given normalization and criteria types.
  • COMET Tools
Class/Function Description Reference
MethodExpert Class which allows to evaluate CO in COMET using any MCDA method. [56]
ManualExpert Class which allows to evaluate CO in COMET manually by pairwise comparisons. [57]
FunctionExpert Class which allows to evaluate CO in COMET using any expert function. [58]
CompromiseExpert Class which allows to evaluate CO in COMET using compromise between several different methods. -
TriadSupportExpert Class which allows to evaluate CO in COMET manually but with triads support. In Press
ESPExpert Class which allows to identify MEJ using expert-defined Expected Solution Points. In Press
triads_consistency Function to which evaluates consistency of the MEJ matrix. [55]
Submodel Class mostly for internal use in StructuralCOMET class. [54]
StructuralCOMET Class which allows to split a decision problem into submodels to be evaluated by the COMET method. [54]

Usage example

Here's a small example of how use this library to solve MCDM problem. For more examples with explanation see examples.

import numpy as np
from pymcdm.methods import TOPSIS
from pymcdm.helpers import rrankdata

# Define decision matrix (2 criteria, 4 alternative)
alts = np.array([
    [4, 4],
    [1, 5],
    [3, 2],
    [4, 2]
], dtype='float')

# Define weights and types
weights = np.array([0.5, 0.5])
types = np.array([1, -1])

# Create object of the method
topsis = TOPSIS()

# Determine preferences and ranking for alternatives
pref = topsis(alts, weights, types)
ranking = rrankdata(pref)

for r, p in zip(ranking, pref):
    print(r, p)

And the output of this example (numbers are rounded):

3 0.6126
4 0.0
2 0.7829
1 1.0

References

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[53] Zavadskas, E. K., Turskis, Z., Antucheviciene, J., & Zakarevicius, A. (2012). Optimization of weighted aggregated sum product assessment. Elektronika ir elektrotechnika, 122(6), 3-6.

[54] Shekhovtsov, A., Kołodziejczyk, J., & Sałabun, W. (2020). Fuzzy model identification using monolithic and structured approaches in decision problems with partially incomplete data. Symmetry, 12(9), 1541.

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