Getting started

pyfdm

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

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

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.