Python 3 library for solving multi-criteria decision-making (MCDM) problems.
You can download and install pymcdm library using pip:
pip install pymcdmThe 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] |
- 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] |
- Helpers
- rankdata
- rrankdata
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
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