pfs-mcdm

Python implementation of multi-criteria decision-making (MCDM) algorithms using pythagorean fuzzy sets (PFSs).

Implemented Algorithms:

• Simple Aggregation
• TOPSIS
• PROMETHEE

Future Work:

• Electre
• COPRAS

For more information about PFSs and the implemented algorithms see:

• Yager, R.R., & Abbasov, A.M. (2013). Pythagorean Membership Grades, Complex Numbers, and Decision Making. International Journal of Intelligent
  Systems, 28, doi:10.1002/int.21584.
• Yager, R.R. (2014). Pythagorean Membership Grades in Multicriteria Decision Making. IEEE Transactions on Fuzzy Systems, 22, 958-965,
  doi:10.1109/TFUZZ.2013.2278989.
• Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of
  Intelligent Systems, 29, doi:10.1002/int.21676.
• Molla, M.U., Giri, B.C., & Biswas, P. (2021). Extended PROMETHEE method with Pythagorean fuzzy sets for medical diagnosis problems. Soft Comput.,
  25, 4503-4512, doi:10.1007/s00500-020-05458-7.
• Ye, J., & Chen, T. (2022). Pythagorean Fuzzy Sets Combined with the PROMETHEE Method for the Selection of Cotton Woven Fabric. Journal of Natural
  Fibers, doi:10.1080/15440478.2022.2072993.

Installation

The pfs-mcdm package can be installed from PyPI using pip for Python 3.

$ pip install pfs-mcdm

How to use?

The decision matrix can be provided as a 2D array-like of tuples. Each tuple represents a pythagorean fuzzy number $(\mu, \nu)$. The weights of the criteria are provided as an 1D array-like of floats. Weights are normalized to sum to 1. Optionally, the aternatives argument can be used to provide alternatives' names.

The output solution is a pandas DataFrame

from pfs_mcdm import simple_aggregation, topsis, promethee

matrix = [ 
[(0.9, 0.3), (0.7, 0.6), (0.5, 0.8), (0.6, 0.3)],
[(0.4, 0.7), (0.9, 0.2), (0.8, 0.1), (0.5, 0.3)],  
[(0.8, 0.4), (0.7, 0.5), (0.6, 0.2), (0.7, 0.4)], 
[(0.7, 0.2), (0.8, 0.2), (0.8, 0.4), (0.6, 0.6)]] 
  
weights = [0.15, 0.25, 0.35, 0.25]  
  
alternatives = ['UNI AIR', 'Transasia', 'Mandarin', 'Daily Air']

Simple Aggregation:

simple_aggregation_sol = simple_aggregation(matrix, weights, alternatives=alternatives)  

print("MCDM solution using simple aggregation:")  
print(simple_aggregation_sol)

MCDM solution using simple aggregation:

	Aggregated	Score	Rank
UNI AIR	(0.635, 0.55)	0.101	4
Transasia	(0.69, 0.265)	0.406	1
Mandarin	(0.68, 0.355)	0.336	3
Daily Air	(0.735, 0.37)	0.403	2

TOPSIS:

topsis_sol = topsis(matrix, weights, alternatives=alternatives)

print("MCDM solution using TOPSIS:")
print(topsis_sol)

MCDM solution using TOPSIS:

	D+	D-	Revised Closeness	Rank
UNI AIR	0.351	0.165	-1.586	4
Transasia	0.175	0.396	0.000	1
Mandarin	0.204	0.359	-0.254	3
Daily Air	0.201	0.316	-0.348	2

PROMETHEE:

The promethee function takes an optional argument preference_func to determine the preference function to be used. Available functions are usual, ushape, vshape, level, and gaussian; default is usual.
  For ushape preference function, an additional argument q can be passed to determine the indifference threshold; default is zero. For vshape and level preference function, additional arguments q and p can be passed to determine the indifference and preference thresholds, respectively; default is zero. For the gaussian preference function, an additional argument s can be passed to determine the Gaussian threshold; default is 0.5.

promethee_sol = promethee(matrix, weights, alternatives=alternatives, preference_func='vshape', q=0.1, p=0.8)  

MCDM solution using PROMETHEE:  
print(promethee_sol)

MCDM solution using PROMETHEE:

	Positive Outranking	Negative Outranking	Net Outranking	Rank
UNI AIR	0.094	0.445	-0.351	4
Transasia	0.291	0.158	0.133	1
Mandarin	0.189	0.137	0.051	3
Daily Air	0.250	0.084	0.167	2

License

MIT