Unweighted VIKOR method

The Unweighted VIKOR method (UW-VIKOR) is a multiple-criteria decision-making (MCDM) technique for ranking alternatives based on the classical VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) approach, however this method does not require the introduction of a priori weighting scheme. Instead, the decision-maker only has to determine the bounds ${(l_j,u_j)}_{j=1}^{M}$ between which the weights vary, thus reducing the demands on the algorithm.

As a consequence, the weights are considered decision variables in a non-linear mathematical optimization problem that considers the VIKOR $Q$-score as the objective function. The optimization yields two scores subjected to maximize ($Q_{i}^{L}$) and minimize ($Q_{i}^{U}$) the $Q$-score per each alternative as well as the optimal weights attached to them ($W_{i}^{L}$ and $W_{i}^{U}$). Then, per each alternative, we get the score intervals $[S_{i}^{L}$, $S_{i}^{U}]$ and $[R_{i}^{L}, R_{i}^{U}]$ by evaluating them with the optimal weights. Finally, we can rank alternatives using an aggregation function of the $[Q_{i}^{L}, Q_{i}^{U}]$ scores.

Installation

You can install the uwVIKOR library from GitHub:

git clone https://github.com/Aaron-AALG/uwVIKOR.git
python3 -m pip install -e uwVIKOR

You can also install it directly from PyPI:

pip install uwVIKOR

Input parameters and Output

Example

The uwVIKOR function is implemented in order to manage decision matrices as input data which will be converted to NumPy arrays. Here is an example in which three alternatives and four criteria are used:

import pandas as pd
import numpy as np
from uwVIKOR.uwVIKOR import *

data = pd.DataFrame({"c1":[173, 176, 142],
                    "c2":[10, 11, 5],
                    "c3":[11.4, 12.3, 8.2],
                    "c4":[10.01, 10.48, 7.3]})
directions = ["max", "max", "min", "min"]
L = np.array([0.1 for _ in range(data.shape[1])])
U = np.array([0.4 for _ in range(data.shape[1])])
v = 0.75

x = uwVIKOR(data, directions, L, U, v)

weights = np.array([0.25, 0.2, 0.2, 0.35])
epsilon = np.finfo(float).eps

try:
    x = uwVIKOR(data,
                directions,
                weights,
                weights + epsilon,
                )
except:
    x = uwVIKOR(data,
                directions,
                weights - epsilon,
                weights,
                )

Optimization in Python

This library uses the minimize function of the scipy.optimize module to carry out the optimization problems. In particular, Q_L and Q_U are obtained one by one, thus we can apply the SLSQP method.