Package: objective-weighting
objective-weightingThe 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.Installationpip install objective-weightingUsageobjective-weightingis 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 matrixmatrixwith 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 typestypes. Criteria types are equal to 1 for profit criteria and -1 for cost criteria. Then you have to calculate criteria weights
using chosen fromweighting_methodsmodule weighting method. Depending on the method chosen, you have to providematrixormatrixandtypesas
weighting method arguments. It is detailed in Usage in the documentation. Then you can evaluate alternatives from the decision matrix using the VIKOR method
frommcda_methodsmodule. The VIKOR method returns a vector with preference valuesprefassigned 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 therank_preferencesmethod provided in theadditionsmodule of theobjective-weightingpackage. Parameterreverse = Falsemeans that alternatives
are sorted in ascending order. Here is an example of using the Entropy weighting methodentropy_weightingfor determining criteria weights and
the VIKOR method to calculate preference values:importnumpyasnpfromobjective_weighting.mcda_methodsimportVIKORfromobjective_weightingimportweighting_methodsasmcda_weightsfromobjective_weightingimportnormalizationsasnormsfromobjective_weighting.additionsimportrank_preferencesmatrix=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 objectvikor=VIKOR(normalization_method=norms.minmax_normalization)# Calculate alternatives preference function values with VIKOR methodpref=vikor(matrix,weights,types)# Rank alternatives according to preference valuesrank=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 namedVIKOR_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_weightsmethod provided by theVIKOR_SMAAclass. In this method, uniform distributed weights
are generated by Monte Carlo simulation. The results of the providedVIKOR_SMAAmethod are Rank acceptability index, Central weight vector, and
Rank scores.Rank acceptability indexThe 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 vectorThe 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 scoresFinal 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 theVIKOR_SMAAmethod:fromobjective_weighting.mcda_methodsimportVIKOR_SMAA# criteria numbern=matrix.shape[1]# SMAA iterations numberiterations=10000# create the VIKOR_SMAA method objectvikor_smaa=VIKOR_SMAA()# generate multiple weight vectors in matrixweight_vectors=vikor_smaa._generate_weights(n,iterations)# run the vikor_smaa methodrank_acceptability_index,central_weight_vector,rank_scores=vikor_smaa(matrix,weight_vectors,types)Licenseobjective-weightingwas created by Aleksandra Bączkiewicz. It is licensed under the terms of the MIT license.DocumentationDocumentation of this library with instruction for installation and usage is
providedhere