# skcriteria.preprocessing.weighters module¶

Functionalities for weight the criteria.

In addition to the main functionality, an MCDA agnostic function is offered to calculate weights to a matrix along an arbitrary axis.

class skcriteria.preprocessing.weighters.SKCWeighterABC[source]

Abstract class capable of determine the weights of the matrix.

This abstract class require to redefine _weight_matrix, instead of _transform_data.

skcriteria.preprocessing.weighters.equal_weights(matrix, base_value=1)[source]

Use the same weights for all criteria.

The result values are normalized by the number of columns.

$w_j = \frac{base\_value}{m}$

Where $m$ is the number os columns/criteria in matrix.

Parameters
• matrix (numpy.ndarray like.) – The matrix of alternatives on which to calculate weights.

• base_value (int or float.) – Value to be normalized by the number of criteria to create the weights.

Returns

array of weights

Return type

numpy.ndarray

Examples

>>> from skcriteria.preprocess import equal_weights
>>> mtx = [[1, 2], [3, 4]]

>>> equal_weights(mtx)
array([0.5, 0.5])

class skcriteria.preprocessing.weighters.EqualWeighter(base_value=1.0)[source]

Assigns the same weights to all criteria.

The algorithm calculates the weights as the ratio of base_value by the total criteria.

property base_value

Value to be normalized by the number of criteria.

skcriteria.preprocessing.weighters.std_weights(matrix)[source]

Calculate weights as the standard deviation of each criterion.

The result is normalized by the number of columns.

$w_j = \frac{base\_value}{m}$

Where $m$ is the number os columns/criteria in matrix.

Parameters

matrix (numpy.ndarray like.) – The matrix of alternatives on which to calculate weights.

Returns

array of weights

Return type

numpy.ndarray

Examples

>>> from skcriteria.preprocess import std_weights
>>> mtx = [[1, 2], [3, 4]]

>>> std_weights(mtx)
array([0.5, 0.5])

class skcriteria.preprocessing.weighters.StdWeighter[source]

Set as weight the normalized standard deviation of each criterion.

skcriteria.preprocessing.weighters.entropy_weights(matrix)[source]

Calculate the weights as the entropy of each criterion.

It uses the underlying scipy.stats.entropy function which assumes that the values of the criteria are probabilities of a distribution.

This routine will normalize the criteria if they don’t sum to 1.

scipy.stats.entropy

Calculate the entropy of a distribution for given probability values.

Examples

>>> from skcriteria.preprocess import entropy_weights
>>> mtx = [[1, 2], [3, 4]]

>>> entropy_weights(mtx)
array([0.46906241, 0.53093759])

class skcriteria.preprocessing.weighters.EntropyWeighter[source]

Assigns the entropy of the criteria as weights.

It uses the underlying scipy.stats.entropy function which assumes that the values of the criteria are probabilities of a distribution.

This transformer will normalize the criteria if they don’t sum to 1.

scipy.stats.entropy

Calculate the entropy of a distribution for given probability values.

skcriteria.preprocessing.weighters.pearson_correlation(arr)[source]

Return Pearson product-moment correlation coefficients.

This function is a thin wrapper of numpy.corrcoef.

Parameters

arr (array like) – A 1-D or 2-D array containing multiple variables and observations. Each row of arr represents a variable, and each column a single observation of all those variables.

Returns

R – The correlation coefficient matrix of the variables.

Return type

numpy.ndarray

numpy.corrcoef

Return Pearson product-moment correlation coefficients.

skcriteria.preprocessing.weighters.spearman_correlation(arr)[source]

Calculate a Spearman correlation coefficient.

This function is a thin wrapper of scipy.stats.spearmanr.

Parameters

arr (array like) – A 1-D or 2-D array containing multiple variables and observations. Each row of arr represents a variable, and each column a single observation of all those variables.

Returns

R – The correlation coefficient matrix of the variables.

Return type

numpy.ndarray

scipy.stats.spearmanr

Calculate a Spearman correlation coefficient with associated p-value.

skcriteria.preprocessing.weighters.critic_weights(matrix, objectives, correlation=<function pearson_correlation>, scale=True)[source]

Execute the CRITIC method without any validation.

class skcriteria.preprocessing.weighters.Critic(correlation='pearson', scale=True)[source]

CRITIC (CRiteria Importance Through Intercriteria Correlation).

The method aims at the determination of objective weights of relative importance in MCDM problems. The weights derived incorporate both contrast intensity and conflict which are contained in the structure of the decision problem.

Parameters
• correlation (str ["pearson" or "spearman"] or callable. (default "pearson")) – This is the correlation function used to evaluate the discordance between two criteria. In other words, what conflict does one criterion a criterion with respect to the decision made by the other criteria. By default the pearson correlation is used, and the kendall correlation is also available implemented. It is also possible to provide a function that receives as a single parameter, the matrix of alternatives, and returns the correlation matrix.

• scale (bool (default True)) – True if it is necessary to scale the data with skcriteria.preprocesisng.cenit_distance prior to calculating the correlation

Warning

UserWarning:

If some objective is to minimize. The original paper only suggests using it against maximization criteria, but there is no real mathematical constraint to use it for minimization.

References

CORRELATION = {'pearson': <function pearson_correlation>, 'spearman': <function spearman_correlation>}
property scale

Return if it is necessary to scale the data.

property correlation

Correlation function.