pyifdm 1.1.1

Python library to support Decision Making with Intuitionistic Fuzzy Sets

pyifdm

Python 3 package to perform Multi-Criteria Decision Analysis in the Intuitionistic Fuzzy environment

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Installation

The package can be download using pip:

pip install pyifdm

Testing

The modules performance can be verified with pytest library

pip install pytest
pytest tests

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Modules and functionalities

• MCDA methods based on Intuitionistic Fuzzy Sets (IFS):

Abbreviation	Full name	Reference
ARAS	Additive Ratio ASsessment	[1]
CODAS	COmbinative Distance-based ASsessment	[2]
COPRAS	COmplex PRoportional ASsessment	[3]
EDAS	Evaluation based on Distance from Average Solution	[4]
MABAC	Multi-Attributive Border Approximation area Comparison	[5]
MAIRCA	MultiAttributive Ideal-Real Comparative Analysis	[6]
MARCOS	Measurement of Alternatives and Ranking according to the Compromise Solution	[31]
MOORA	Multi-Objective Optimization Method by Ratio Analysis	[7]
OCRA	Operational Competitiveness Rating	[30]
TOPSIS	Technique for the Order of Prioritisation by Similarity to Ideal Solution	[8]
VIKOR	VIseKriterijumska Optimizacija I Kompromisno Resenje	[9]
WASPAS	Weighted Aggregated Sum Product Assessment	[38]
WSM	Weighted Sum Method	[37]
WPM	Weighted Product Method	[37]

• Weighting methods:

Name	Reference
Burillo entropy weights	[25]
Equal weights	[10]
Entropy weights	[9]
Liu entropy weights	[27]
Szmidt entropy weights	[26]
Thakur entropy weights	[3]
Ye entropy weights	[24]

• Normalization methods:

Name	Reference
Ecer normalization	[10]
Max normalization	[37]
Min-Max normalization	[6]
Supriya normalization	[11]
Swap normalization	[2]

• Score functions:

Name	Reference
Chen score 1	[29]
Chen score 2	[29]
Kharal score 1	[15]
Kharal score 2	[15]
Liu Wang score	[28]
Supriya score	[11]
Thakur score	[3]
Wan Dong score 1	[13]
Wan Dong score 2	[13]
Wei score	[12]
Zhang Xu score 1	[14]
Zhang Xu score 2	[14]

• Distance measures:

Name	Reference
Euclidean distance	[16]
Grzegorzewski distance	[17]
Hamming distance	[16]
Hausdorf Euclidean distance	[32]
Luo Distance	[9]
Normalized Euclidean distance	[16]
Normalized Hamming distance	[16]
Wang Xin distance 1	[18]
Wang Xin distance 2	[18]
Yang Chiclana distance	[19]

• IFS-similarity measures:

Name	Reference
Chen similarity	[38]
Fan-Zhang similarity	[38]
Hong-Kim similarity	[38]
Li similarity	[38]
Li-Xu similarity	[38]
Ye similarity	[38]

• Correlation coefficients:

Name	Reference
Pearson correlation coefficient	[21]
Spearman correlation coefficient	[20]
Weighted Spearman correlation coefficient	[22]
WS Rank Similarity coefficient	[23]

• Intuitionistic Fuzzy Set [33], [34], [35], [36] :

Functionality name
Addition
Subtraction
Multiplication
Division
Power
Equality
AND (Intersection)
OR (Union)
Invert
OWA aggregation
Dominance
Jaccard similarity
Fuzzy relation

• Graphs:

Functionality name
IFS criteria bar plot
IFS heatmap plot
IFS radar plot
Single IFS bar plot
Single IFS pie plot

• Helpers methods
  • rank
  • generate ifs matrix

Usage example

Below the sample example of the Intuitionistic Fuzzy EDAS method application is presented. More examples of package functionalities can be found in Jupyter examples.

from pyifdm.methods import ifEDAS
from pyifdm.helpers import rank
import numpy as np

if __name__ == '__main__':
    matrix = np.array([
        [[0.4745, 0.5255], [0.4752, 0.5248], [0.2981, 0.7019], [0.4374, 0.5627]],
        [[0.5346, 0.4654], [0.5532, 0.4468], [0.6300, 0.3700], [0.5901, 0.4099]],
        [[0.4324, 0.5676], [0.4030, 0.5970], [0.4298, 0.5702], [0.4361, 0.5639]],
        [[0.5235, 0.4765], [0.4808, 0.5192], [0.5667, 0.4333], [0.2913, 0.7087]],
        [[0.4168, 0.5832], [0.4923, 0.5077], [0.4732, 0.5268], [0.4477, 0.5523]]
    ])

    weights = np.array([0.2, 0.3, 0.15, 0.35])

    types = np.array([1, -1, 1, 1])

    if_edas = ifEDAS()
    pref = if_edas(matrix, weights, types)

    print(f'IF-EDAS preferences: {pref}')
    print(f'IF-EDAS ranking: {rank(pref)}')

Output:

IF-EDAS preferences: 0.276 0.259 0.523 0.995 0.322
IF-EDAS ranking: 4 5 2 1 3

References

[1] Raj Mishra, A., Sisodia, G., Raj Pardasani, K., & Sharma, K. (2020). Multi-criteria IT personnel selection on intuitionistic fuzzy information measures and ARAS methodology. Iranian Journal of Fuzzy Systems, 17(4), 55-68.

[2] Buyukozkan, G., & Göçer, F. (2019, August). Prioritizing the strategies to enhance smart city logistics by intuitionistic fuzzy CODAS. In 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019) (pp. 805-811). Atlantis Press.

[3] Thakur, P., Kizielewicz, B., Gandotra, N., Shekhovtsov, A., Saini, N., Saeid, A. B., & Sałabun, W. (2021). A New Entropy Measurement for the Analysis of Uncertain Data in MCDA Problems Using Intuitionistic Fuzzy Sets and COPRAS Method. Axioms, 10(4), 335.

[4] Liang, Y. (2020). An EDAS method for multiple attribute group decision-making under intuitionistic fuzzy environment and its application for evaluating green building energy-saving design projects. Symmetry, 12(3), 484.

[5] Li, Y. (2021). IF-MABAC Method for Evaluating the Intelligent Transportation System with Intuitionistic Fuzzy Information. Journal of Mathematics, 2021.

[7] Ecer, F. (2022). An extended MAIRCA method using intuitionistic fuzzy sets for coronavirus vaccine selection in the age of COVID-19. Neural Computing and Applications, 34(7), 5603-5623.

[8] Pérez-Domínguez, L., Alvarado-Iniesta, A., Rodríguez-Borbón, I., & Vergara-Villegas, O. (2015). Intuitionistic fuzzy MOORA for supplier selection. Dyna, 82(191), 34-41.

[9] Boran, F. E., Boran, K. U. R. T. U. L. U. Ş., & Menlik, T. (2012). The evaluation of renewable energy technologies for electricity generation in Turkey using intuitionistic fuzzy TOPSIS. Energy Sources, Part B: Economics, Planning, and Policy, 7(1), 81-90.

[10] Ying-Yu, W., & De-Jian, Y. (2011, September). Extended VIKOR for multi-criteria decision making problems under intuitionistic environment. In 2011 International Conference on Management Science & Engineering 18th Annual Conference Proceedings (pp. 118-122). IEEE.

[11] Ecer, F., & Pamucar, D. (2021). MARCOS technique under intuitionistic fuzzy environment for determining the COVID-19 pandemic performance of insurance companies in terms of healthcare services. Applied Soft Computing, 104, 107199.

[12] De, S. K., Biswas, R., & Roy, A. R. (2000). Some operations on intuitionistic fuzzy sets. Fuzzy sets and Systems, 114(3), 477-484.

[13] Wei P, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis 27:571–574

[14] Wan, S., & Dong, J. (2020). A selection method based on MAGDM with interval-valued intuitionistic fuzzy sets. In Decision Making Theories and Methods Based on Interval-Valued Intuitionistic Fuzzy Sets (pp. 115-137). Springer, Singapore.

[15] Zhang, X., & Xu, Z. (2012). A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making, 11(2), 135-146.

[16] Kharal, A. (2009). Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy, 98(1), 35-39.

[17] Çalı, S., & Balaman, Ş. Y. (2019). A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment. Expert Systems with Applications, 119, 36-50.

[18] Grzegorzewski, P. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy sets and systems, 148(2), 319-328.

[19] Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern recognition letters, 26(13), 2063-2069.

[19] Yang, Y., & Chiclana, F. (2012). Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Systems with Applications, 39(10), 8665-8670.

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

[21] 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.

[22] 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.

[23] 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.

[24] Ye, J. Two effective measures of intuitionistic fuzzy entropy. Computing 2010, 87, 55–62.

[25] Burillo, P.; Bustince, H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 1996, 78, 305–316.

[26] Szmidt, E.; Kacprzyk, J. Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 2001, 118, 467–477.

[27] Liu, M.; Ren, H. A new intuitionistic fuzzy entropy and application in multi-attribute decision making. Information 2014, 5, 587–601.

[28] Liu, H. W., & Wang, G. J. (2007). Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research, 179(1), 220-233.

[29] Chen, T. Y. (2011). A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings. Information Sciences, 181(17), 3652-3676.

[30] Mishra, A. R., Rani, P., Cavallaro, F., Hezam, I. M., & Lakshmi, J. (2023). An integrated intuitionistic fuzzy closeness coefficient-based OCRA method for sustainable urban transportation options selection. Axioms, 12(2), 144.

[31] Ecer, F., & Pamucar, D. (2021). MARCOS technique under intuitionistic fuzzy environment for determining the COVID-19 pandemic performance of insurance companies in terms of healthcare services. Applied Soft Computing, 104, 107199.

[32] Li, M., Wu, C., Zhang, L., & You, L. N. (2015). An intuitionistic fuzzy-TODIM method to solve distributor evaluation and selection problem. International Journal of Simulation Modelling, 14(3), 511-524.

[33] Ejegwa, P. A., Akowe, S. O., Otene, P. M., & Ikyule, J. M. (2014). An overview on intuitionistic fuzzy sets. Int. J. Sci. Technol. Res, 3(3), 142-145.

[34] Du, W. S. (2021). Subtraction and division operations on intuitionistic fuzzy sets derived from the Hamming distance. Information Sciences, 571, 206-224.

[35] Mitchell, H. B. (2004). An intuitionistic OWA operator. International journal of uncertainty, fuzziness and knowledge-based systems, 12(06), 843-860.

[36] Ngan, S. C. (2016). An activation detection based similarity measure for intuitionistic fuzzy sets. Expert Systems with Applications, 60, 62-80.

[37] Xiong, L., Zhong, S., Liu, S., Zhang, X., & Li, Y. (2020). An approach for resilient-green supplier selection based on WASPAS, BWM, and TOPSIS under intuitionistic fuzzy sets. Mathematical Problems in Engineering, 2020.

[38] Mishra, A. R., Singh, R. K., & Motwani, D. (2019). Multi-criteria assessment of cellular mobile telephone service providers using intuitionistic fuzzy WASPAS method with similarity measures. Granular Computing, 4, 511-529.