mcdm

Python implementation of multiple-criteria decision-making algorithms

Installation

The mcdm package can be installed from PyPI using pip for Python 3:

$ pip3 install mcdm

Alternatively, you can install the latest version of the mcdm package from its GitHub repository:

$ git clone https://github.com/akestoridis/mcdm.git
$ cd mcdm/
$ pip3 install .

If an old unsupported version of a dependency was already installed on your system and you cannot or do not want to upgrade it, then you can avoid the dependency conflict by installing the mcdm package in a Python 3 virtual environment as follows:

$ python3 -m venv venv/
$ source venv/bin/activate
(venv) $ pip install --upgrade pip
(venv) $ pip install mcdm

If, for some reason, a future supported version of a dependency contains breaking changes, then you can use the requirements.txt file to install the exact version that was last used to test the mcdm package, e.g.:

$ git clone https://github.com/akestoridis/mcdm.git
$ cd mcdm/
$ python3 -m venv venv/
$ source venv/bin/activate
(venv) $ pip install --upgrade pip
(venv) $ pip install -r requirements.txt
(venv) $ pip install .

Features

The following tables include the scoring, weighting, correlation, and normalization methods that are supported by the mcdm package.

Scoring methods

Short Name	Full Name	References
SAW	Simple Additive Weighting	[1], [2]
MEW	Multiplicative Exponential Weighting	[2]
TOPSIS	Technique for Order Preference by Similarity to Ideal Solution	[1]
mTOPSIS	Modified Technique for Order Preference by Similarity to Ideal Solution	[3]

Weighting methods

Short Name	Full Name	References
MW	Mean Weights	[4]
EM	Entropy Measure	[1], [3]
SD	Standard Deviation	[4]
CRITIC	Criteria Importance Through Intercriteria Correlation	[4]
VIC	Variability and Interdependencies of Criteria	[5]

Correlation methods

Short Name	Full Name	References
Pearson	Pearson Correlation Coefficients	[6]
AbsPearson	Absolute Value of the Pearson Correlation Coefficients	[6]
dCor	Distance Correlation Coefficients	[7], [8]

Normalization methods

Short Name	Full Name	References
Linear1	Linear Normalization (1)	[1], [9]
Linear2	Linear Normalization (2)	[1], [9]
Linear3	Linear Normalization (3)	[1], [9]
Vector	Vector Normalization	[1], [9]

Usage

After importing the mcdm package, you can view its contents using the built-in help function:

>>> import mcdm
>>> help(mcdm)

The contents of its subpackages can be viewed similarly, e.g.:

>>> help(mcdm.weighting)

The mcdm package can compute the ranking of alternatives, which are provided as an array_like object, with its rank function. By default, the rank function is using the SAW scoring method, the MW weighting method, and assumes that the decision matrix contains unnamed alternatives with normalized benefit criteria:

>>> x_matrix = [
...     [0.00, 1.00],
...     [0.25, 0.75],
...     [0.50, 0.50],
...     [0.75, 0.25],
...     [1.00, 0.00],
... ]
>>> mcdm.rank(x_matrix)
[('a1', 0.5), ('a2', 0.5), ('a3', 0.5), ('a4', 0.5), ('a5', 0.5)]

You can select the use of the MEW scoring method, without changing the remaining default selections, as follows:

>>> x_matrix = [
...     [0.00, 1.00],
...     [0.25, 0.75],
...     [0.50, 0.50],
...     [0.75, 0.25],
...     [1.00, 0.00],
... ]
>>> mcdm.rank(x_matrix, s_method="MEW")
[('a3', 0.5000000000000001), ('a2', 0.4330127018922193), ('a4', 0.4330127018922193), ('a1', 0.0), ('a5', 0.0)]

Alternatively, you can use the TOPSIS scoring method with predefined weights as follows:

>>> x_matrix = [
...     [0.00, 1.00],
...     [0.25, 0.75],
...     [0.50, 0.50],
...     [0.75, 0.25],
...     [1.00, 0.00],
... ]
>>> mcdm.rank(x_matrix, w_vector=[0.7, 0.3], s_method="TOPSIS")
[('a5', 0.7), ('a4', 0.6504133360970108), ('a3', 0.5), ('a2', 0.3495866639029891), ('a1', 0.3)]

You can also use the TOPSIS scoring method with a mixture of benefit and cost criteria as follows:

>>> x_matrix = [
...     [0.00, 1.00],
...     [0.25, 0.75],
...     [0.50, 0.50],
...     [0.75, 0.25],
...     [1.00, 0.00],
... ]
>>> mcdm.rank(x_matrix, is_benefit_x=[True, False], s_method="TOPSIS")
[('a5', 1.0), ('a4', 0.75), ('a3', 0.5), ('a2', 0.25000000000000006), ('a1', 0.0)]

Alternatively, you can use the TOPSIS scoring method, the SD weighting method, and the Vector normalization method with named alternatives as follows:

>>> x_matrix = [
...     [4,  5, 10],
...     [3, 10,  6],
...     [3, 20,  2],
...     [2, 15,  5],
... ]
>>> alt_names = ["A", "B", "C", "D"]
>>> mcdm.rank(x_matrix, alt_names=alt_names, n_method="Vector", w_method="SD", s_method="TOPSIS")
[('A', 0.5623140105790617), ('D', 0.472563994792934), ('C', 0.4474283120076966), ('B', 0.43874437587505694)]

Similarly, you can use the SAW scoring method, the CRITIC weighting method, and the Linear2 normalization method with named alternatives as follows:

>>> x_matrix = [
...     [4,  5, 10],
...     [3, 10,  6],
...     [3, 20,  2],
...     [2, 15,  5],
... ]
>>> alt_names = ["A", "B", "C", "D"]
>>> mcdm.rank(x_matrix, alt_names=alt_names, n_method="Linear2", w_method="CRITIC", s_method="SAW")
[('C', 0.5864039798997854), ('A', 0.5363555775174913), ('B', 0.42272592958624855), ('D', 0.41815995516110754)]

Furthermore, you can use the mTOPSIS scoring method, the EM weighting method, and the Linear3 normalization method with named alternatives as follows:

>>> x_matrix = [
...     [4,  5, 10],
...     [3, 10,  6],
...     [3, 20,  2],
...     [2, 15,  5],
... ]
>>> alt_names = ["A", "B", "C", "D"]
>>> mcdm.rank(x_matrix, alt_names=alt_names, n_method="Linear3", w_method="EM", s_method="mTOPSIS")
[('A', 0.5671982017516887), ('D', 0.4737709007480381), ('B', 0.44023602515388915), ('C', 0.43979056725587967)]

In addition, you can use the MEW scoring method, the VIC weighting method, and the Linear1 normalization method with named alternatives as follows:

>>> x_matrix = [
...     [4,  5, 10],
...     [3, 10,  6],
...     [3, 20,  2],
...     [2, 15,  5],
... ]
>>> alt_names = ["A", "B", "C", "D"]
>>> mcdm.rank(x_matrix, alt_names=alt_names, n_method="Linear1", w_method="VIC", s_method="MEW")
[('A', 0.596199006150288), ('B', 0.5926510141687035), ('D', 0.5816528401371021), ('C', 0.507066254464828)]

Finally, you can use the load function of the mcdm package to load a decision matrix from a text file (e.g., the example09.tsv file), and then compute the ranking of its alternatives using the MEW scoring method and the VIC weighting method as follows:

>>> x_matrix, alt_names = mcdm.load("./mcdm/tests/data/example09.tsv", delimiter="\t", skiprows=1, labeled_rows=True)
>>> mcdm.rank(x_matrix, alt_names=alt_names, w_method="VIC", s_method="MEW")
[('COORD.PRoPHET', 0.47540101629920883), ('DF.PRoPHET', 0.4720540449389032), ('CnR.LTS', 0.38076976314696165), ('SimBetTS.L8', 0.3800058193419937), ('SimBetTS.L16', 0.3799920328578032), ('CnR.DestEnc', 0.37944808013507936), ('LSF-SnW.L16', 0.37739981242275067), ('DF.DestEnc', 0.3737879965369727), ('COORD.DestEnc', 0.3735362169300779), ('SimBetTS.L4', 0.372439515643607), ('LSF-SnW.L8', 0.3689450285406012), ('DF.LTS', 0.36604297140966213), ('COORD.LTS', 0.36532018876831296), ('LSF-SnW.L4', 0.34498575401083065), ('CnF.PRoPHET', 0.344899433667112), ('CnF.DestEnc', 0.34080904510687654), ('CnF.LTS', 0.33682425293123014), ('SnF.L8', 0.3338134560941729), ('SnF.L4', 0.3310799577048607), ('CnR.PRoPHET', 0.3283706628162786), ('SnF.L2', 0.3282710142810222), ('SnF.L16', 0.325965295985982), ('SimBetTS.L2', 0.3198197170434966), ('LSF-SnW.L2', 0.28336307866897725), ('CnR.Enc', 0.25388909503755097), ('DF.Enc', 0.19642752820544426), ('COORD.Enc', 0.18527125018989776), ('Epidemic', 0.17618218317052287), ('Direct', 0.14463684900589485), ('EBR.L16', 0.14427544773753895), ('SnW.L16', 0.14419569083973272), ('EBR.L2', 0.139576851541699), ('SnW.L2', 0.1393465080643217), ('SnW.L8', 0.13728835719879856), ('EBR.L8', 0.13728300706136987), ('EBR.L4', 0.13654721879934206), ('SnW.L4', 0.1364251455180083), ('CnF.Enc', 0.11713353969310777)]

References

[1] C.-L. Hwang and K. Yoon, Multiple Attribute Decision Making, ser. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag Berlin Heidelberg, 1981, vol. 186, isbn: 9783540105589.

[2] S. H. Zanakis, A. Solomon, N. Wishart, and S. Dublish, “Multi-attribute decision making: A simulation comparison of select methods,” Eur. J. Oper. Res., vol. 107, no. 3, pp. 507–529, 1998, doi: 10.1016/S0377-2217(97)00147-1.

[3] H. Deng, C.-H. Yeh, and R. J. Willis, “Inter-company comparison using modified TOPSIS with objective weights,” Comput. Oper. Res., vol. 27, no. 10, pp. 963–973, 2000, doi: 10.1016/S0305-0548(99)00069-6.

[4] D. Diakoulaki, G. Mavrotas, and L. Papayannakis, “Determining objective weights in multiple criteria problems: The CRITIC method,” Comput. Oper. Res., vol. 22, no. 7, pp. 763–770, 1995, doi: 10.1016/0305-0548(94)00059-H.

[5] D.-G. Akestoridis and E. Papapetrou, “A framework for the evaluation of routing protocols in opportunistic networks,” Comput. Commun., vol. 145, pp. 14–28, 2019, doi: 10.1016/j.comcom.2019.06.003.

[6] J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist., vol. 42, no. 1, pp. 59–66, 1988, doi: 10.2307/2685263.

[7] G. J. Székely, M. L. Rizzo, and N. K. Bakirov, “Measuring and testing dependence by correlation of distances,” Ann. Statist., vol. 35, no. 6, pp. 2769–2794, 2007, doi: 10.1214/009053607000000505.

[8] G. J. Székely and M. L. Rizzo, “Brownian distance covariance,” Ann. Appl. Statist., vol. 3, no. 4, pp. 1236–1265, 2009, doi: 10.1214/09-AOAS312.

[9] H.-S. Shih, H.-J. Shyur, and E. S. Lee, “An extension of TOPSIS for group decision making,” Math. Comput. Model., vol. 45, no. 7–8, pp. 801–813, 2007, doi: 10.1016/j.mcm.2006.03.023.

License

This project is licensed under the terms of the MIT License (MIT).