| Name | pymcdm JSON |
| Version |
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| Summary | Python library for Multi-Criteria Decision-Making |
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| author | None |
| requires_python | >=3.11 |
| license | None |
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# PyMCDM
Python 3 library for solving multi-criteria decision-making (MCDM) problems.
Documentation is avaliable on [readthedocs](https://pymcdm.readthedocs.io/en/master/).
___
# Installation
You can download and install `pymcdm` library using pip:
```Bash
pip install pymcdm
```
You can run all tests with following command from the root of the project:
```Bash
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._](https://doi.org/10.1016/j.softx.2023.101368)"
Or using BibTex:
```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](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]](#c1) |
| VIKOR | VIseKriterijumska Optimizacija I Kompromisno Resenje | [[2]](#c2) |
| COPRAS | COmplex PRoportional ASsessment | [[3]](#c3) |
| PROMETHEE I & II | Preference Ranking Organization METHod for Enrichment of Evaluations I & II | [[4]](#c4) |
| COMET | Characteristic Objects Method | [[5]](#c5) |
| SPOTIS | Stable Preference Ordering Towards Ideal Solution | [[6]](#c6) |
| ARAS | Additive Ratio ASsessment | [[7]](#c7),[[8]](#c8) |
| COCOSO | COmbined COmpromise SOlution | [[9]](#c9) |
| CODAS | COmbinative Distance-based ASsessment | [[10]](#c10) |
| EDAS | Evaluation based on Distance from Average Solution | [[11]](#c11),[[12]](#c12) |
| MABAC | Multi-Attributive Border Approximation area Comparison | [[13]](#c13) |
| MAIRCA | MultiAttributive Ideal-Real Comparative Analysis | [[14]](#c14),[[15]](#c15),[[16]](#c16) |
| MARCOS | Measurement Alternatives and Ranking according to COmpromise Solution | [[17]](#c17),[[18]](#c18) |
| OCRA | Operational Competitiveness Ratings | [[19]](#c19),[[20]](#c20) |
| MOORA | Multi-Objective Optimization Method by Ratio Analysis | [[21]](#c21),[[22]](#c22) |
| RIM | Reference Ideal Method | [[48]](#c48) |
| ERVD | Election Based on relative Value Distances | [[49]](#c49) |
| PROBID | Preference Ranking On the Basis of Ideal-average Distance | [[50]](#c50) |
| WSM | Weighted Sum Model | [[51]](#c51) |
| WPM | Weighted Product Model | [[52]](#c52) |
| WASPAS | Weighted Aggregated Sum Product ASSessment | [[53]](#c53) |
| RAM | Root Assesment Method | [[62]](#c62) |
* Weighting methods:
| Acronym | Method Name | Reference |
|----------- |--------------------------------------------------------- |:----------------------------------------: |
| - | Equal/Mean weights | [[23]](#c23) |
| - | Entropy weights | [[23]](#c23),[[24]](#c24),[[25]](#c25) |
| STD | Standard Deviation weights | [[23]](#c23),[[26]](#c26) |
| MEREC | MEthod based on the Removal Effects of Criteria | [[27]](#c27) |
| CRITIC | CRiteria Importance Through Intercriteria Correlation | [[28]](#c28),[[29]](#c29) |
| CILOS | Criterion Impact LOS | [[30]](#c30) |
| IDOCRIW | Integrated Determination of Objective CRIteria Weight | [[30]](#c30) |
| - | Angular/Angle weights | [[31]](#c31) |
| - | Gini Coeficient weights | [[32]](#c32) |
| - | Statistical variance weights | [[33]](#c33) |
* Normalization methods:
| Method Name | Reference |
|-------------------------------------- |:--------------------------: |
| Weitendorf’s Linear Normalization | [[34]](#c34) |
| Maximum - Linear Normalization | [[35]](#c35) |
| Sum-Based Linear Normalization | [[36]](#c36) |
| Vector Normalization | [[36]](#c36),[[37]](#c37) |
| Logarithmic Normalization | [[36]](#c36),[[37]](#c37) |
| Linear Normalization (Max-Min) | [[34]](#c34),[[38]](#c38) |
| Non-linear Normalization (Max-Min) | [[39]](#c39) |
| Enhanced Accuracy Normalization | [[40]](#c40) |
| Lai and Hwang Normalization | [[38]](#c38) |
| Zavadskas and Turskis Normalization | [[38]](#c38) |
* Correlation coefficients:
| Coefficient name | Reference |
|---------------------------------------------------- |:-------------------------: |
| Spearman's rank correlation coefficient | [[41]](#c41),[[42]](#c42) |
| Pearson correlation coefficient | [[43]](#c43) |
| Weighted Spearman’s rank correlation coefficient | [[44]](#c44) |
| Rank Similarity Coefficient | [[45]](#c45) |
| Kendall rank correlation coefficient | [[46]](#c46) |
| Goodman and Kruskal's gamma | [[47]](#c47) |
| Drastic Weighted Similarity (draWS) | [[59]](#c59) |
| Weights Similarity Coefficient (WSC) | [[60]](#c60) |
| Weights Similarity Coefficient 2 (WSC2) | [[60]](#c60) |
* 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]](#c56) |
| `ManualExpert` | Class which allows to evaluate CO in COMET manually by pairwise comparisons. | [[57]](#c57) |
| `FunctionExpert` | Class which allows to evaluate CO in COMET using any expert function. | [[58]](#c58) |
| `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. | [[61]](#c61) |
| `triads_consistency` | Function to which evaluates consistency of the MEJ matrix. | [[55]](#c55) |
| `Submodel` | Class mostly for internal use in StructuralCOMET class. | [[54]](#c54) |
| `StructuralCOMET` | Class which allows to split a decision problem into submodels to be evaluated by the COMET method. | [[54]](#c54) |
___
# Usage example
Here's a small example of how use this library to solve MCDM problem.
For more examples with explanation see [examples](https://gitlab.com/shekhand/mcda/-/blob/master/examples/examples.ipynb).
```python
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):
```bash
3 0.6126
4 0.0
2 0.7829
1 1.0
```
---
# References
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"description": "# PyMCDM\n\nPython 3 library for solving multi-criteria decision-making (MCDM) problems.\n\nDocumentation is avaliable on [readthedocs](https://pymcdm.readthedocs.io/en/master/).\n\n___\n\n# Installation\n\nYou can download and install `pymcdm` library using pip:\n\n```Bash\npip install pymcdm\n```\n\nYou can run all tests with following command from the root of the project:\n\n```Bash\npython -m unittest -v\n```\n\n___\n\n# Citing pymcdm\n\nIf usage of the pymcdm library lead to a scientific publication, please \nacknowledge this fact by citing \"[_Kizielewicz, B., Shekhovtsov, A., \n& Sa\u0142abun, W. (2023). pymcdm\u2014The universal library for solving multi-criteria \ndecision-making problems. SoftwareX, 22, 101368._](https://doi.org/10.1016/j.softx.2023.101368)\"\n\nOr using BibTex:\n```bibtex\n@article{kizielewicz2023pymcdm,\n title={pymcdm\u2014The universal library for solving multi-criteria decision-making problems},\n author={Kizielewicz, Bart{\\l}omiej and Shekhovtsov, Andrii and Sa{\\l}abun, Wojciech},\n journal={SoftwareX},\n volume={22},\n pages={101368},\n year={2023},\n publisher={Elsevier}\n}\n```\n\nDOI: [https://doi.org/10.1016/j.softx.2023.101368](https://doi.org/10.1016/j.softx.2023.101368)\n\n___\n\n# Available methods\n\nThe library contains:\n\n* MCDA methods:\n\n| Acronym \t| Method Name | Reference |\n| :-------------------- | --------------------------------------------------------------------------------- | :--------------------------------------: |\n| TOPSIS \t| Technique for the Order of Prioritisation by Similarity to Ideal Solution | [[1]](#c1) |\n| VIKOR \t| VIseKriterijumska Optimizacija I Kompromisno Resenje | [[2]](#c2) |\n| COPRAS \t| COmplex PRoportional ASsessment | [[3]](#c3) |\n| PROMETHEE I & II \t| Preference Ranking Organization METHod for Enrichment of Evaluations I & II | [[4]](#c4) |\n| COMET \t| Characteristic Objects Method | [[5]](#c5) |\n| SPOTIS \t| Stable Preference Ordering Towards Ideal Solution | [[6]](#c6) |\n| ARAS \t| Additive Ratio ASsessment | [[7]](#c7),[[8]](#c8) |\n| COCOSO \t| COmbined COmpromise SOlution | [[9]](#c9) |\n| CODAS \t| COmbinative Distance-based ASsessment | [[10]](#c10) |\n| EDAS \t| Evaluation based on Distance from Average Solution | [[11]](#c11),[[12]](#c12) |\n| MABAC \t| Multi-Attributive Border Approximation area Comparison | [[13]](#c13) |\n| MAIRCA \t| MultiAttributive Ideal-Real Comparative Analysis | [[14]](#c14),[[15]](#c15),[[16]](#c16) |\n| MARCOS \t| Measurement Alternatives and Ranking according to COmpromise Solution | [[17]](#c17),[[18]](#c18) |\n| OCRA \t| Operational Competitiveness Ratings | [[19]](#c19),[[20]](#c20) |\n| MOORA \t| Multi-Objective Optimization Method by Ratio Analysis | [[21]](#c21),[[22]](#c22) |\n| RIM \t| Reference Ideal Method | [[48]](#c48) |\n| ERVD \t| Election Based on relative Value Distances | [[49]](#c49) |\n| PROBID | Preference Ranking On the Basis of Ideal-average Distance | [[50]](#c50) |\n| WSM | Weighted Sum Model | [[51]](#c51) |\n| WPM | Weighted Product Model | [[52]](#c52) |\n| WASPAS | Weighted Aggregated Sum Product ASSessment | [[53]](#c53) |\n| RAM \t| Root Assesment Method | [[62]](#c62) |\n\n* Weighting methods:\n\n| Acronym \t| Method Name \t| Reference \t|\n|-----------\t|---------------------------------------------------------\t|:----------------------------------------:\t|\n| - \t| Equal/Mean weights \t| [[23]](#c23) \t|\n| - \t| Entropy weights \t| [[23]](#c23),[[24]](#c24),[[25]](#c25) \t|\n| STD \t| Standard Deviation weights \t| [[23]](#c23),[[26]](#c26) \t|\n| MEREC \t| MEthod based on the Removal Effects of Criteria \t| [[27]](#c27) \t|\n| CRITIC \t| CRiteria Importance Through Intercriteria Correlation \t| [[28]](#c28),[[29]](#c29) \t|\n| CILOS \t| Criterion Impact LOS \t| [[30]](#c30) \t|\n| IDOCRIW \t| Integrated Determination of Objective CRIteria Weight \t| [[30]](#c30) \t|\n| - \t| Angular/Angle weights \t| [[31]](#c31) \t|\n| - \t| Gini Coeficient weights \t| [[32]](#c32) \t|\n| - \t| Statistical variance weights \t| [[33]](#c33) \t|\n\n* Normalization methods:\n\n| Method Name \t| Reference \t|\n|--------------------------------------\t|:--------------------------:\t|\n| Weitendorf\u2019s Linear Normalization \t| [[34]](#c34) \t|\n| Maximum - Linear Normalization \t| [[35]](#c35) \t|\n| Sum-Based Linear Normalization \t| [[36]](#c36) \t|\n| Vector Normalization \t| [[36]](#c36),[[37]](#c37) \t|\n| Logarithmic Normalization \t| [[36]](#c36),[[37]](#c37) \t|\n| Linear Normalization (Max-Min) \t| [[34]](#c34),[[38]](#c38) \t|\n| Non-linear Normalization (Max-Min) \t| [[39]](#c39) \t|\n| Enhanced Accuracy Normalization \t| [[40]](#c40) \t|\n| Lai and Hwang Normalization | [[38]](#c38) |\n| Zavadskas and Turskis Normalization | [[38]](#c38) |\n\n* Correlation coefficients:\n\n| Coefficient name \t| Reference \t|\n|----------------------------------------------------\t|:-------------------------:\t|\n| Spearman's rank correlation coefficient \t| [[41]](#c41),[[42]](#c42) \t|\n| Pearson correlation coefficient \t| [[43]](#c43) \t|\n| Weighted Spearman\u2019s rank correlation coefficient \t| [[44]](#c44) \t|\n| Rank Similarity Coefficient \t| [[45]](#c45) \t|\n| Kendall rank correlation coefficient \t| [[46]](#c46) \t|\n| Goodman and Kruskal's gamma \t| [[47]](#c47) \t|\n| Drastic Weighted Similarity (draWS) | [[59]](#c59) \t|\n| Weights Similarity Coefficient (WSC) | [[60]](#c60) \t|\n| Weights Similarity Coefficient 2 (WSC2) | [[60]](#c60) \t|\n\n* Helpers\n\n| Helpers submodule | Description |\n|--------------------- |------------ |\n| `rankdata` | Create ranking vector from the preference vector. Smaller preference values has higher positions in the ranking. |\n| `rrankdata` | Alias to the `rankdata` which reverse the sorting order. |\n| `correlation_matrix` | Create the correlation matrix for given coefficient from several the several rankings. |\n| `normalize_matrix` | Normalize decision matrix column by column using given normalization and criteria types. |\n\n* COMET Tools\n\n| Class/Function | Description | Reference |\n|----------------------|----------------------------------------------------------------------------------------------------|:-------------:|\n| `MethodExpert` | Class which allows to evaluate CO in COMET using any MCDA method. | [[56]](#c56) |\n| `ManualExpert` | Class which allows to evaluate CO in COMET manually by pairwise comparisons. | [[57]](#c57) |\n| `FunctionExpert` | Class which allows to evaluate CO in COMET using any expert function. | [[58]](#c58) |\n| `CompromiseExpert` | Class which allows to evaluate CO in COMET using compromise between several different methods. | - |\n| `TriadSupportExpert` | Class which allows to evaluate CO in COMET manually but with triads support. | In Press |\n| `ESPExpert` | Class which allows to identify MEJ using expert-defined Expected Solution Points. | [[61]](#c61) |\n| `triads_consistency` | Function to which evaluates consistency of the MEJ matrix. | [[55]](#c55) |\n| `Submodel` | Class mostly for internal use in StructuralCOMET class. | [[54]](#c54) |\n| `StructuralCOMET` | Class which allows to split a decision problem into submodels to be evaluated by the COMET method. | [[54]](#c54) |\n\n\n___\n# Usage example\n\nHere's a small example of how use this library to solve MCDM problem.\nFor more examples with explanation see [examples](https://gitlab.com/shekhand/mcda/-/blob/master/examples/examples.ipynb).\n\n```python\nimport numpy as np\nfrom pymcdm.methods import TOPSIS\nfrom pymcdm.helpers import rrankdata\n\n# Define decision matrix (2 criteria, 4 alternative)\nalts = np.array([\n [4, 4],\n [1, 5],\n [3, 2],\n [4, 2]\n], dtype='float')\n\n# Define weights and types\nweights = np.array([0.5, 0.5])\ntypes = np.array([1, -1])\n\n# Create object of the method\ntopsis = TOPSIS()\n\n# Determine preferences and ranking for alternatives\npref = topsis(alts, weights, types)\nranking = rrankdata(pref)\n\nfor r, p in zip(ranking, pref):\n print(r, p)\n```\n\nAnd the output of this example (numbers are rounded):\n\n```bash\n3 0.6126\n4 0.0\n2 0.7829\n1 1.0\n```\n---\n# References\n\n<a name=\"c1\">[1]</a> Hwang, C. L., & Yoon, K. (1981). Methods for multiple attribute decision making. In Multiple attribute decision making (pp. 58-191). Springer, Berlin, Heidelberg.\n\n<a name=\"c2\">[2]</a> Duckstein, L., & Opricovic, S. (1980). Multiobjective optimization in river basin development. Water resources research, 16(1), 14-20.\n\n<a name=\"c3\">[3]</a> Zavadskas, E. K., Kaklauskas, A., Peldschus, F., & Turskis, Z. (2007). Multi-attribute assessment of road design solutions by using the COPRAS method. The Baltic Journal of Road and Bridge Engineering, 2(4), 195-203.\n\n<a name=\"c4\">[4]</a> Brans, J. P., Vincke, P., & Mareschal, B. (1986). How to select and how to rank projects: The PROMETHEE method. European journal of operational research, 24(2), 228-238.\n\n<a name=\"c5\">[5]</a> Sa\u0142abun, W., Karczmarczyk, A., W\u0105tr\u00f3bski, J., & Jankowski, J. (2018, November). Handling data uncertainty in decision making with COMET. 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