objective-weighting

The Python 3 Library of Objective Weighting Techniques for MCDA methods.

This library provides 11 objective criteria weighting methods and a Stochastic Multicriteria Acceptability Analysis Method (SMAA) that does not require criteria weights.

Installation

pip install objective-weighting

Usage

objective-weighting is the Python 3 package that provides 11 objective weighting methods, which can be used to determine criteria weights for solving multi-criteria problems with Multi-Criteria Decision Analysis (MCDA) methods. The first step is providing the decision matrix matrix with alternatives performance values. The decision matrix is two-dimensional and contains m alternatives in rows and n criteria in columns. You also have to provide criteria types types. Criteria types are equal to 1 for profit criteria and -1 for cost criteria. Then you have to calculate criteria weights using chosen from weighting_methods module weighting method. Depending on the method chosen, you have to provide matrix or matrix and types as weighting method arguments. It is detailed in Usage in the documentation. Then you can evaluate alternatives from the decision matrix using the VIKOR method from mcda_methods module. The VIKOR method returns a vector with preference values pref assigned to alternatives. To rank alternatives according to VIKOR preference values, you have to sort them in ascending order because, in the VIKOR method, the best alternative has the lowest preference value. The alternatives are ranked using the rank_preferences method provided in the additions module of the objective-weighting package. Parameter reverse = False means that alternatives are sorted in ascending order. Here is an example of using the Entropy weighting method entropy_weighting for determining criteria weights and the VIKOR method to calculate preference values:

import numpy as np
from objective_weighting.mcda_methods import VIKOR
from objective_weighting import weighting_methods as mcda_weights
from objective_weighting import normalizations as norms
from objective_weighting.additions import rank_preferences

matrix = np.array([[256, 8, 41, 1.6, 1.77, 7347.16],
[256, 8, 32, 1.0, 1.8, 6919.99],
[256, 8, 53, 1.6, 1.9, 8400],
[256, 8, 41, 1.0, 1.75, 6808.9],
[512, 8, 35, 1.6, 1.7, 8479.99],
[256, 4, 35, 1.6, 1.7, 7499.99]])

types = np.array([1, 1, 1, 1, -1, -1])
weights = mcda_weights.entropy_weighting(matrix)

# Create the VIKOR method object
vikor = VIKOR(normalization_method=norms.minmax_normalization)
# Calculate alternatives preference function values with VIKOR method
pref = vikor(matrix, weights, types)
# Rank alternatives according to preference values
rank = rank_preferences(pref, reverse = False)

Stochastic Multicriteria Acceptability Analysis Method (SMAA)

Additionally, the objective-weighting library provides the Stochastic Multicriteria Acceptability Analysis Method (SMAA), which, combined with the VIKOR method, is designed to solve decision problems when there is a lack of information about criteria preferences (unknown criteria weights). This method is implemented in the class named VIKOR_SMAA. This method requires only the decision matrix, a matrix with weight vectors and criteria types provided in one call. The number of weight vectors is equal to the number of iterations. First, the matrix with weight vectors must be generated with _generate_weights method provided by the VIKOR_SMAA class. In this method, uniform distributed weights are generated by Monte Carlo simulation. The results of the provided VIKOR_SMAA method are Rank acceptability index, Central weight vector, and Rank scores.

Rank acceptability index

The ranking is built based on generated weights. Next, counters for corresponding ranks in relation to the alternatives are increased. After a given number of iterations, the rank acceptability indexes are obtained by dividing the counters by the number of iterations. Rank acceptability index shows the share of different scores placing an alternative in a given rank.

Central weight vector

The central weights are calculated similarly. In each iteration, the weight vector is added to its ‘summed weight vector’ when the alternative gets the rank. Next, this vector is divided by the number of iterations to get the central weight vector. The central weight vector describes the preferences of a typical decision-maker, supporting this alternative with the assumed preference model. It allows the decision-maker to see what criteria preferences result in the best evaluation of given alternatives.

Rank scores

Final ranking of alternatives provided by the ranking function, which adds to each alternative value of 1 each time it has better preference values than each other.

Here is example of use of the VIKOR_SMAA method:

from objective_weighting.mcda_methods import VIKOR_SMAA

# criteria number
n = matrix.shape[1]
# SMAA iterations number
iterations = 10000

# create the VIKOR_SMAA method object
vikor_smaa = VIKOR_SMAA()

# generate multiple weight vectors in matrix
weight_vectors = vikor_smaa._generate_weights(n, iterations)

# run the vikor_smaa method
rank_acceptability_index, central_weight_vector, rank_scores = vikor_smaa(matrix, weight_vectors, types)

License

objective-weighting was created by Aleksandra Bączkiewicz. It is licensed under the terms of the MIT license.

Documentation

Documentation of this library with instruction for installation and usage is provided here