pymcdm 1.2.1

Python library for Multi-Criteria Decision-Making

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]

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

• 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.	[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 (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

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References

[1] Hwang, C. L., & Yoon, K. (1981). Methods for multiple attribute decision making. In Multiple attribute decision making (pp. 58-191). Springer, Berlin, Heidelberg.

[2] Duckstein, L., & Opricovic, S. (1980). Multiobjective optimization in river basin development. Water resources research, 16(1), 14-20.

[3] 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.

[4] 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.

[5] Sałabun, W., Karczmarczyk, A., Wątróbski, J., & Jankowski, J. (2018, November). Handling data uncertainty in decision making with COMET. In 2018 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1478-1484). IEEE.

[6] Dezert, J., Tchamova, A., Han, D., & Tacnet, J. M. (2020, July). The spotis rank reversal free method for multi-criteria decision-making support. In 2020 IEEE 23rd International Conference on Information Fusion (FUSION) (pp. 1-8). IEEE.

[7] Zavadskas, E. K., & Turskis, Z. (2010). A new additive ratio assessment (ARAS) method in multicriteria decision‐making. Technological and economic development of economy, 16(2), 159-172.

[8] Stanujkic, D., Djordjevic, B., & Karabasevic, D. (2015). Selection of candidates in the process of recruitment and selection of personnel based on the SWARA and ARAS methods. Quaestus, (7), 53.

[9] Yazdani, M., Zarate, P., Zavadskas, E. K., & Turskis, Z. (2019). A Combined Compromise Solution (CoCoSo) method for multi-criteria decision-making problems. Management Decision.

[10] Badi, I., Shetwan, A. G., & Abdulshahed, A. M. (2017, September). Supplier selection using COmbinative Distance-based ASsessment (CODAS) method for multi-criteria decision-making. In Proceedings of The 1st International Conference on Management, Engineering and Environment (ICMNEE) (pp. 395-407).

[11] Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica, 26(3), 435-451.

[12] Yazdani, M., Torkayesh, A. E., Santibanez-Gonzalez, E. D., & Otaghsara, S. K. (2020). Evaluation of renewable energy resources using integrated Shannon Entropy—EDAS model. Sustainable Operations and Computers, 1, 35-42.

[13] Pamučar, D., & Ćirović, G. (2015). The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert systems with applications, 42(6), 3016-3028.

[14] Gigović, L., Pamučar, D., Bajić, Z., & Milićević, M. (2016). The combination of expert judgment and GIS-MAIRCA analysis for the selection of sites for ammunition depots. Sustainability, 8(4), 372.

[15] Pamucar, D. S., Pejcic Tarle, S., & Parezanovic, T. (2018). New hybrid multi-criteria decision-making DEMATELMAIRCA model: sustainable selection of a location for the development of multimodal logistics centre. Economic research-Ekonomska istraživanja, 31(1), 1641-1665.

[16] Aksoy, E. (2021). An Analysis on Turkey's Merger and Acquisition Activities: MAIRCA Method. Gümüşhane Üniversitesi Sosyal Bilimler Enstitüsü Elektronik Dergisi, 12(1), 1-11.

[17] Stević, Ž., Pamučar, D., Puška, A., & Chatterjee, P. (2020). Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS). Computers & Industrial Engineering, 140, 106231.

[18] Ulutaş, A., Karabasevic, D., Popovic, G., Stanujkic, D., Nguyen, P. T., & Karaköy, Ç. (2020). Development of a novel integrated CCSD-ITARA-MARCOS decision-making approach for stackers selection in a logistics system. Mathematics, 8(10), 1672.

[19] Parkan, C. (1994). Operational competitiveness ratings of production units. Managerial and Decision Economics, 15(3), 201-221.

[20] Işık, A. T., & Adalı, E. A. (2016). A new integrated decision making approach based on SWARA and OCRA methods for the hotel selection problem. International Journal of Advanced Operations Management, 8(2), 140-151.

[21] Brauers, W. K. (2003). Optimization methods for a stakeholder society: a revolution in economic thinking by multi-objective optimization (Vol. 73). Springer Science & Business Media.

[22] Hussain, S. A. I., & Mandal, U. K. (2016). Entropy based MCDM approach for Selection of material. In National Level Conference on Engineering Problems and Application of Mathematics (pp. 1-6).

[23] Sałabun, W., Wątróbski, J., & Shekhovtsov, A. (2020). Are mcda methods benchmarkable? a comparative study of topsis, vikor, copras, and promethee ii methods. Symmetry, 12(9), 1549.

[24] Lotfi, F. H., & Fallahnejad, R. (2010). Imprecise Shannon’s entropy and multi attribute decision making. Entropy, 12(1), 53-62.

[25] Li, X., Wang, K., Liu, L., Xin, J., Yang, H., & Gao, C. (2011). Application of the entropy weight and TOPSIS method in safety evaluation of coal mines. Procedia engineering, 26, 2085-2091.

[26] Wang, Y. M., & Luo, Y. (2010). Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making. Mathematical and Computer Modelling, 51(1-2), 1-12.

[27] Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2021). Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC). Symmetry, 13(4), 525.

[28] Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763-770.

[29] Tuş, A., & Adalı, E. A. (2019). The new combination with CRITIC and WASPAS methods for the time and attendance software selection problem. Opsearch, 56(2), 528-538.

[30] Zavadskas, E. K., & Podvezko, V. (2016). Integrated determination of objective criteria weights in MCDM. International Journal of Information Technology & Decision Making, 15(02), 267-283.

[31] Shuai, D., Zongzhun, Z., Yongji, W., & Lei, L. (2012, May). A new angular method to determine the objective weights. In 2012 24th Chinese Control and Decision Conference (CCDC) (pp. 3889-3892). IEEE.

[32] Li, G., & Chi, G. (2009, December). A new determining objective weights method-gini coefficient weight. In 2009 First International Conference on Information Science and Engineering (pp. 3726-3729). IEEE.

[33] Rao, R. V., & Patel, B. K. (2010). A subjective and objective integrated multiple attribute decision making method for material selection. Materials & Design, 31(10), 4738-4747.

[34] Brauers, W. K., & Zavadskas, E. K. (2006). The MOORA method and its application to privatization in a transition economy. Control and cybernetics, 35, 445-469.

[35] Jahan, A., & Edwards, K. L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design (1980-2015), 65, 335-342.

[36] Gardziejczyk, W., & Zabicki, P. (2017). Normalization and variant assessment methods in selection of road alignment variants–case study. Journal of civil engineering and management, 23(4), 510-523.

[37] Zavadskas, E. K., & Turskis, Z. (2008). A new logarithmic normalization method in games theory. Informatica, 19(2), 303-314.

[38] Jahan, A., & Edwards, K. L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design (1980-2015), 65, 335-342.

[39] Peldschus, F., Vaigauskas, E., & Zavadskas, E. K. (1983). Technologische entscheidungen bei der berücksichtigung mehrerer Ziehle. Bauplanung Bautechnik, 37(4), 173-175.

[40] Zeng, Q. L., Li, D. D., & Yang, Y. B. (2013). VIKOR method with enhanced accuracy for multiple criteria decision making in healthcare management. Journal of medical systems, 37(2), 1-9.

[41] Binet, A., & Henri, V. (1898). La fatigue intellectuelle (Vol. 1). Schleicher frères.

[42] Spearman, C. (1910). Correlation calculated from faulty data. British Journal of Psychology, 1904‐1920, 3(3), 271-295.

[43] Pearson, K. (1895). VII. Note on regression and inheritance in the case of two parents. proceedings of the royal society of London, 58(347-352), 240-242.

[44] Dancelli, L., Manisera, M., & Vezzoli, M. (2013). On two classes of Weighted Rank Correlation measures deriving from the Spearman’s ρ. In Statistical Models for Data Analysis (pp. 107-114). Springer, Heidelberg.

[45] Sałabun, W., & Urbaniak, K. (2020, June). A new coefficient of rankings similarity in decision-making problems. In International Conference on Computational Science (pp. 632-645). Springer, Cham.

[46] Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81-93.

[47] Goodman, L. A., & Kruskal, W. H. (1979). Measures of association for cross classifications. Measures of association for cross classifications, 2-34.

[48] Cables, E., Lamata, M. T., & Verdegay, J. L. (2016). RIM-reference ideal method in multicriteria decision making. Information Sciences, 337, 1-10.

[49] Shyur, H. J., Yin, L., Shih, H. S., & Cheng, C. B. (2015). A multiple criteria decision making method based on relative value distances. Foundations of Computing and Decision Sciences, 40(4), 299-315.

[50] Wang, Z., Rangaiah, G. P., & Wang, X. (2021). Preference ranking on the basis of ideal-average distance method for multi-criteria decision-making. Industrial & Engineering Chemistry Research, 60(30), 11216-11230.

[51] Fishburn, P. C., Murphy, A. H., & Isaacs, H. H. (1968). Sensitivity of decisions to probability estimation errors: A reexamination. Operations Research, 16(2), 254-267.

[52] Fishburn, P. C., Murphy, A. H., & Isaacs, H. H. (1968). Sensitivity of decisions to probability estimation errors: A reexamination. Operations Research, 16(2), 254-267.

[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.

[55] Sałabun, W., Shekhovtsov, A., & Kizielewicz, B. (2021, June). A new consistency coefficient in the multi-criteria decision analysis domain. In Computational Science–ICCS 2021: 21st International Conference, Krakow, Poland, June 16–18, 2021, Proceedings, Part I (pp. 715-727). Cham: Springer International Publishing.

[56] Paradowski, B., Bączkiewicz, A., & Watrąbski, J. (2021). Towards proper consumer choices-MCDM based product selection. Procedia Computer Science, 192, 1347-1358.

[57] Sałabun, W. (2015). The characteristic objects method: A new distance‐based approach to multicriteria decision‐making problems. Journal of Multi‐Criteria Decision Analysis, 22(1-2), 37-50.

[58] Sałabun, W., & Piegat, A. (2017). Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artificial Intelligence Review, 48, 557-571.

[59] Sałabun, W., & Shekhovtsov, A. (2023, September). An Innovative Drastic Metric for Ranking Similarity in Decision-Making Problems. In 2023 18th Conference on Computer Science and Intelligence Systems (FedCSIS) (pp. 731-738). IEEE.

[60] Shekhovtsov, A. (2023). Evaluating the Performance of Subjective Weighting Methods for Multi-Criteria Decision-Making using a novel Weights Similarity Coefficient. Procedia Computer Science, 225, 4785-4794.

[61] Shekhovtsov, A., Kizielewicz, B., & Sałabun, W. (2023). Advancing individual decision-making: An extension of the characteristic objects method using expected solution point. Information Sciences, 647, 119456.

[62] Sotoudeh-Anvari, A. (2023). Root Assessment Method (RAM): a novel multi-criteria decision making method and its applications in sustainability challenges. Journal of Cleaner Production, 423, 138695.