pyfdm 1.1.11

Python library for Fuzzy Decision Making

pyfdm

Python 3 package with Fuzzy Decision Making (PyFDM) methods based on Triangular Fuzzy Numbers (TFN)

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Installation

The package can be download using pip:

pip install pyfdm

Testing

The modules performance can be verified with pytest library

pip install pytest
pytest tests

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Citations

If you are using this library in your research work to calculate results with Fuzzy MCDA approach, cite with APA format :

"Więckowski, J., Kizielewicz, B., & Sałabun, W. (2022). pyFDM: A Python library for uncertainty decision analysis methods. SoftwareX, 20, 101271."

or with BibTex :

@article{wikeckowski2022pyfdm,
  title={pyFDM: A Python library for uncertainty decision analysis methods},
  author={Wi{\k{e}}ckowski, Jakub and Kizielewicz, Bart{\l}omiej and Sa{\l}abun, Wojciech},
  journal={SoftwareX},
  volume={20},
  pages={101271},
  year={2022},
  publisher={Elsevier}
}

Modules and functionalities

• Fuzzy MCDA methods:

Abbreviation	Full name	Reference
ARAS	Additive Ratio ASsessment	[1]
COCOSO	Combined Compromise Solution	[32]
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]
MOORA	Multi-Objective Optimization Method by Ratio Analysis	[7]
OCRA	Operational Competitiveness Ratings	[8]
SPOTIS	Stable Preference Ordering Towards Ideal Solution	[25]
TOPSIS	Technique for the Order of Prioritisation by Similarity to Ideal Solution	[9]
VIKOR	VIseKriterijumska Optimizacija I Kompromisno Resenje	[10]
WASPAS	Weighted Aggregated Sum Product Assessment	[26]
WPM	Weighted Product Model	[27]
WSM	Weighted Sum Model	[27]

• Weighting methods:

Name	Reference
Equal weights	[11]
Shannon entropy weights	[12]
Standard deviation weights	[13]
Variance weights	[14]

• Normalization methods:

Name	Reference
COCOSO Normalization	[32]
Linear Normalization	[15]
Max Normalization	[2]
Min-Max Normalization	[5]
SAW Normalization	[3], [24]
Sum Normalization	[1]
Sqrt Normalization	[31]
Vector Normalization	[7]
WASPAS Normalization	[26]

• Defuzzification methods:

Name	Reference
Bisector defuzzification	[29]
Graded mean average defuzzification	[4]
Height defuzzification	[29]
Largest of Maximum defuzzification	[29]
Mean defuzzification	[16] [17]
Mean area defuzzification	[15]
Smallest of Maximum defuzzification	[29]
Weighted mean defuzzification	[10]

• Distance measures:

Name	Reference
Canberra distance	[30]
Chebyshev distance	[30]
Euclidean distance	[18]
Hamming distance	[19]
Mahdavi distance	[18]
L-R distance	[19]
Tran Duckstein distance	[19]
Vertex distance	[15]
Weighted Euclidean distance	[15]
Weighted Hamming distance	[15]

• Correlation coefficients:

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

• Triangular Fuzzy Number [28] :

Functionality name
Addition
Subtractions
Multiplication
Division
Absolute value
Equality
Less equal comparison
Greater equal comparison
Round value
Membership function
Centroid
Core
Inclusion
S-norm operator
T-norm operator

• Graphs:

Functionality name
Multiple TFNs plot
Single TFN plot
S-norm operator plot
T-norm operator plot
TFN criteria plot
TFN membership plot

• Helpers methods
  • rank
  • generate_fuzzy_matrix

Usage example

Below the sample example of the package functionalities is presented. More usage examples of available methods are presented in Jupyter examples.

from pyfdm.methods import fARAS
import numpy as np

if __name__ == '__main__':
    matrix = np.array([
        [[5, 7, 9], [5, 7, 9], [7, 9, 9]],
        [[1, 3, 5], [3, 5, 7], [3, 5, 7]],
        [[1, 1, 3], [1, 3, 5], [1, 3, 5]],
        [[7, 9, 9], [7, 9, 9], [7, 9, 9]]
    ])

    weights = np.array([[5, 7, 9], [7, 9, 9], [3, 5, 7]])
    types = np.array([1, -1, 1])

    f_aras = fARAS()
    pref = f_aras(matrix, weights, types)

    print(f'Fuzzy ARAS preferences: {pref}')
    print(f'Fuzzy ARAS ranking: {f_aras.rank()}')

Output:

Fuzzy ARAS preferences: 1.011 0.854 1.312 0.993
Fuzzy ARAS ranking: 2 4 1 3

References

[1] Fu, Y. K., Wu, C. J., & Liao, C. N. (2021). Selection of in-flight duty-free product suppliers using a combination fuzzy AHP, fuzzy ARAS, and MSGP methods. Mathematical Problems in Engineering, 2021.

[2]Panchal, D., Chatterjee, P., Shukla, R. K., Choudhury, T., & Tamosaitiene, J. (2017). Integrated Fuzzy AHP-Codas Framework for Maintenance Decision in Urea Fertilizer Industry. Economic Computation & Economic Cybernetics Studies & Research, 51(3).

[3] Narang, M., Joshi, M. C., & Pal, A. K. (2021). A hybrid fuzzy COPRAS-base-criterion method for multi-criteria decision making. Soft Computing, 25(13), 8391-8399.

[4] Zindani, D., Maity, S. R., & Bhowmik, S. (2019). Fuzzy-EDAS (evaluation based on distance from average solution) for material selection problems. In Advances in Computational Methods in Manufacturing (pp. 755-771). Springer, Singapore.

[5] Bozanic, D., Tešić, D., & Milićević, J. (2018). A hybrid fuzzy AHP-MABAC model: Application in the Serbian Army–The selection of the location for deep wading as a technique of crossing the river by tanks. Decision Making: Applications in Management and Engineering, 1(1), 143-164.

[6] Boral, S., Howard, I., Chaturvedi, S. K., McKee, K., & Naikan, V. N. A. (2020). An integrated approach for fuzzy failure modes and effects analysis using fuzzy AHP and fuzzy MAIRCA. Engineering Failure Analysis, 108, 104195.

[7] Karande, P., & Chakraborty, S. (2012). A Fuzzy-MOORA approach for ERP system selection. Decision Science Letters, 1(1), 11-21.

[8] ULUTAŞ, A. (2019). Supplier selection by using a fuzzy integrated model for a textile company. Engineering Economics, 30(5), 579-590.

[9] Chen, C. T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy sets and systems, 114(1), 1-9.

[10] Opricovic, S. (2007). A fuzzy compromise solution for multicriteria problems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(03), 363-380.

[11] Iskander, M. G. (2002). Comparison of fuzzy numbers using possibility programming: comments and new concepts. Computers & Mathematics with Applications, 43(6-7), 833-840.

[12] Kacprzak, D. (2017). Objective weights based on ordered fuzzy numbers for fuzzy multiple criteria decision-making methods. Entropy, 19(7), 373.

[13] 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.

[14] Bikmukhamedov, R., Yeryomin, Y., & Seitz, J. (2016, July). Evaluation of MCDA-based handover algorithms for mobile networks. In 2016 Eighth International Conference on Ubiquitous and Future Networks (ICUFN) (pp. 810-815). IEEE.

[15] Roszkowska, E., & Wachowicz, T. (2015). Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems. European Journal of Operational Research, 242(3), 920-932.

[16] Yılmaz, M., & Atan, T. (2021). Hospital site selection using fuzzy EDAS method: case study application for districts of Istanbul. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-12.

[17] Zolfani, S. H., Görçün, Ö. F., & Küçükönder, H. (2021). Evaluating logistics villages in Turkey using hybrid improved fuzzy SWARA (IMF SWARA) and fuzzy MABAC techniques. Technological and Economic Development of Economy, 27(6), 1582-1612.

[18] Wang, H., Lu, X., Du, Y., Zhang, C., Sadiq, R., & Deng, Y. (2017). Fault tree analysis based on TOPSIS and triangular fuzzy number. International journal of system assurance engineering and management, 8(4), 2064-2070.

[19] Talukdar, P., & Dutta, P. A Comparative Study of TOPSIS Method via Different Distance Measure.

[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] Saifullah, S. (2021). Fuzzy-AHP approach using Normalized Decision Matrix on Tourism Trend Ranking based-on Social Media. arXiv preprint arXiv:2102.04222.

[25] Shekhovtsov, A., Paradowski, B., Więckowski, J., Kizielewicz, B., & Sałabun, W. (2022, December). Extension of the SPOTIS method for the rank reversal free decision-making under fuzzy environment. In 2022 IEEE 61st Conference on Decision and Control (CDC) (pp. 5595-5600). IEEE.

[26] Turskis, Z., Zavadskas, E. K., Antuchevičienė, J., & Kosareva, N. (2015). A hybrid model based on fuzzy AHP and fuzzy WASPAS for construction site selection.

[27] Triantaphyllou, E., & Lin, C. T. (1996). Development and evaluation of five fuzzy multiattribute decision-making methods. international Journal of Approximate reasoning, 14(4), 281-310.

[28] Sudha, T., & Jayalalitha, G. (2020, July). Fuzzy triangular numbers in-Sierpinski triangle and right angle triangle. In Journal of Physics: Conference Series (Vol. 1597, No. 1, p. 012022). IOP Publishing.

[29] Berkachy, R., & Donzé, L. (2016). Linguistic questionnaire evaluation: an application of the signed distance defuzzification method on different fuzzy numbers. The impact on the skewness of the output distributions. International Journal of Fuzzy Systems and Advanced Applications, 3, 12-19.

[30] Rodrigues, É. O. (2018). Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier. Pattern Recognition Letters, 110, 66-71.

[31] Kizielewicz, B., & Bączkiewicz, A. (2021). Comparison of Fuzzy TOPSIS, Fuzzy VIKOR, Fuzzy WASPAS and Fuzzy MMOORA methods in the housing selection problem. Procedia Computer Science, 192, 4578-4591.

[32] Ulutaş, A., Popovic, G., Radanov, P., Stanujkic, D., & Karabasevic, D. (2021). A new hybrid fuzzy PSI-PIPRECIA-CoCoSo MCDM based approach to solving the transportation company selection problem. Technological and Economic Development of Economy, 27(5), 1227-1249.