pymcdm 1.4.0

Python library for Multi-Criteria Decision-Making

Important: Development process was moved from GitLab to Github.

PyMCDM

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

Documentation is avaliable on readthedocs.

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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

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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

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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]
RAM	Root Assesment Method	[62]
RAFSI	Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval	[69]
LoPM	Limits on Property Method	[67]
LMAW	Logarithmic Methodology of Additive Weights	[70]
AROMAN	Alternative Ranking Order Method Accounting for Two-Step Normalization)	[72]

• MCDA Methods' extensions and variations:

Acronym	Reference
Balanced SPOTIS	[68]

• 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]
LOPCOW	LOgarithmic Percentage Change-driven Objective Weighting	[71]
-	Angular/Angle weights	[31]
-	Gini Coeficient weights	[32]
-	Statistical variance weights	[33]
AHP	Analytic Hierarchy Process	[65]
RANCOM	RANking COMparison	[66]

• 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)	[59]
Weights Similarity Coefficient (WSC)	[60]
Weights Similarity Coefficient 2 (WSC2)	[60]

• Distance metrics:

Metric Name	Reference
Kemeny distance	[73]
Frobenius distance	[74]
draWS distance	[75]

• 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.	[63]
TriadSupportExpert	Class which allows to evaluate CO in COMET manually but with triads support.	[64]
ESPExpert	Class which allows to identify MEJ using expert-defined Expected Solution Points.	[61]
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]

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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 (3 criteria, 4 alternative)
alts = np.array([
    [4, 4, 0.2],
    [1, 5, 0.5],
    [3, 2, 0.3],
    [4, 3, 0.5]
])

# Define criteria weights (should sum up to 1)
weights = np.array([0.3, 0.5, 0.2])

# Define criteria types (1 for profit, -1 for cost)
types = np.array([1, -1, 1])

# Create object of the method
# Note, that default normalization method for TOPSIS is minmax
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 0.469
4.0 0.255
1.0 0.765
2.0 0.747

If you want to inspect computation process in details, you can add the following code to the above example:

results = topsis(alts, weights, types, verbose=True)
print(results)

This will produce output that contains formatted decision matrix, intermediate results, preference values and ranking.

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References

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