Usage

Installation

To use evo-spotis, first install it using the pip command, as demonstrated below.

pip install evo-spotis

Usage examples

The SPOTIS method

The SPOTIS method is used to calculate the preference of evaluated alternatives. The SPOTIS method requires providing the decision matrix matrix, vector with criteria weights weights, and vector with criteria types types and minimum and maximum bounds of alternatives performance values for particular criteria. The SPOTIS method returns a vector with preference values pref. To generate the SPOTIS ranking of alternatives, pref has to be sorted in ascending order. The ranking is generated by rank_preferences, providing pref as argument and setting parameter reverse as False because we need to sort preferences ascendingly.

import numpy as np
from evo_spotis.mcda_methods import SPOTIS
from evo_spotis.additions import rank_preferences

# provide decision matrix in array numpy.darray
matrix = np.array([[15000, 4.3, 99, 42, 737],
[15290, 5.0, 116, 42, 892],
[15350, 5.0, 114, 45, 952],
[15490, 5.3, 123, 45, 1120]])

# provide criteria weights in array numpy.darray. All weights must sum to 1.
weights = np.array([0.2941, 0.2353, 0.2353, 0.0588, 0.1765])

# provide criteria types in array numpy.darray. Profit criteria are represented by 1 and cost criteria by -1.
types = np.array([-1, -1, -1, 1, 1])

# Determine minimum bounds of performance values for each criterion in decision matrix
bounds_min = np.array([14000, 3, 80, 35, 650])

# Determine maximum bounds of performance values for each criterion in decision matrix
bounds_max = np.array([16000, 8, 140, 60, 1300])

# Stack minimum and maximum bounds vertically using vstack. You will get a matrix that has two rows and a number of columns equal to the number of criteria
bounds = np.vstack((bounds_min, bounds_max))

# Create the SPOTIS method object
spotis = SPOTIS()

# Calculate the SPOTIS preference values of alternatives
pref = spotis(matrix, weights, types, bounds)

# Generate ranking of alternatives by sorting alternatives ascendingly according to the SPOTIS algorithm (reverse = False means sorting in ascending order) according to preference values
rank = rank_preferences(pref, reverse = False)

print('Preference values: ', np.round(pref, 4))
print('Ranking: ', rank)

Output

Preference values:  [0.478  0.5781 0.5557 0.5801]
Ranking:  [1 3 2 4]

Stochastic algorithm

The Differential Evolution algorithm DE_algorithm for criteria weights prediction

import numpy as np
from evo_spotis.stochastic_algorithms import DE_algorithm

# Create object of the DE_algorithm
de_algorithm = DE_algorithm()
# run DE algorithm providing decision matrix with training dataset `X_train`, target variable of training dataset `y_train` (ranking), criteria types `types` and `bounds` for the SPOTIS method
# de_algorithm returns `BestSolution` representing predicted criteria weights and the best `BestFitness` and mean `MeanFitness` goal (fitness) fucntion values
BestSolution, BestFitness, MeanFitness = de_algorithm(X_train, y_train, types, bounds)

Correlation coefficents

Spearman correlation coefficient

This method is used to calculate correlation between two different rankings. It requires two vectors R and Q with rankings of the same size. It returns value of correlation.

import numpy as np
from evo_spotis import correlations as corrs

# Provide two vectors with rankings obtained with different MCDA methods
R = np.array([1, 2, 3, 4, 5])
Q = np.array([1, 3, 2, 4, 5])

# Calculate the correlation using `spearman` coefficient
coeff = corrs.spearman(R, Q)
print('Spearman coeff: ', np.round(coeff, 4))

Output

Spearman coeff:  0.9

Weighted Spearman correlation coefficient

This method is used to calculate correlation between two different rankings. It requires two vectors R and Q with rankings of the same size. It returns value of correlation.

import numpy as np
from evo_spotis import correlations as corrs

# Provide two vectors with rankings obtained with different MCDA methods
R = np.array([1, 2, 3, 4, 5])
Q = np.array([1, 3, 2, 4, 5])

# Calculate the correlation using `weighted_spearman` coefficient
coeff = corrs.weighted_spearman(R, Q)
print('Weighted Spearman coeff: ', np.round(coeff, 4))

Output

Weighted Spearman coeff:  0.8833

Pearson correlation coefficient

This method is used to calculate correlation between two different rankings. It requires two vectors R and Q with rankings of the same size. It returns value of correlation.

import numpy as np
from evo_spotis import correlations as corrs

# Provide two vectors with rankings obtained with different MCDA methods
R = np.array([1, 2, 3, 4, 5])
Q = np.array([1, 3, 2, 4, 5])

# Calculate the correlation using `pearson_coeff` coefficient
coeff = corrs.pearson_coeff(R, Q)
print('Pearson coeff: ', np.round(coeff, 4))

Output

Pearson coeff:  0.9

Objective method for criteria weights determination

Entropy weighting method

This method is used to calculate criteria weights based on alternatives perfromance values provided in decision matrix. This method requires providing two-dimensional decision matrix matrix with perfromance values of alternatives in rows considering criteria in columns. It returns vector with criteria weights. All values in vector weights must sum to 1.

import numpy as np
from evo_spotis import weighting_methods as mcda_weights

matrix = np.array([[30, 30, 38, 29],
[19, 54, 86, 29],
[19, 15, 85, 28.9],
[68, 70, 60, 29]])

weights = mcda_weights.entropy_weighting(matrix)

print('Entropy weights: ', np.round(weights, 4))

Output

Entropy weights:  [0.463  0.3992 0.1378 0.    ]

Methods for decision matrix normalization

Here is an example of vector normalization usage. Other normalizations provided in module normalizations, namely minmax_normalization, max_normalization, sum_normalization, linear_normalization, multimoora_normalization are used in analogous way.

Vector normalization

This method is used to normalize decision matrix matrix. It requires providing decision matrix matrix with performance values of alternatives in rows considering criteria in columns and vector with criteria types types. This method returns normalized matrix.

import numpy as np
from evo_spotis import normalizations as norms

matrix = np.array([[8, 7, 2, 1],
[5, 3, 7, 5],
[7, 5, 6, 4],
[9, 9, 7, 3],
[11, 10, 3, 7],
[6, 9, 5, 4]])

types = np.array([1, 1, 1, 1])

norm_matrix = norms.vector_normalization(matrix, types)
print('Normalized matrix: ', np.round(norm_matrix, 4))

Output

Normalized matrix:  [[0.4126 0.3769 0.1525 0.0928]
 [0.2579 0.1615 0.5337 0.4642]
 [0.361  0.2692 0.4575 0.3714]
 [0.4641 0.4845 0.5337 0.2785]
 [0.5673 0.5384 0.2287 0.6499]
 [0.3094 0.4845 0.3812 0.3714]]