# skcriteria.preprocessing.distance module¶

Normalization through the distance to distance function.

skcriteria.preprocessing.distance.cenit_distance(matrix, objectives)[source]

Calculate a scores with respect to an ideal and anti-ideal alternative.

For every criterion $$f$$ of this multicriteria problem we define a membership function $$x_j$$ mapping the values of $$f_j$$ to the interval [0, 1].

The result score $$x_{aj}$$ is close to the ideal value $$f_{j}^*$$, which is the best performance in criterion , and far from the anti-ideal value $$f_{j^*}$$, which is the worst performance in criterion $$j$$. Both ideal and anti-ideal, are achieved by at least one of the alternatives under consideration.

$x_{aj} = \frac{f_j(a) - f_{j^*}}{f_{j}^* - f_{j^*}}$
class skcriteria.preprocessing.distance.CenitDistance[source]

Relative scores with respect to an ideal and anti-ideal alternative.

For every criterion $$f$$ of this multicriteria problem we define a membership function $$x_j$$ mapping the values of $$f_j$$ to the interval [0, 1].

The result score $$x_{aj}$$ is close to the ideal value $$f_{j}^*$$, which is the best performance in criterion , and far from the anti-ideal value $$f_{j^*}$$, which is the worst performance in criterion $$j$$. Both ideal and anti-ideal, are achieved by at least one of the alternatives under consideration.

$x_{aj} = \frac{f_j(a) - f_{j^*}}{f_{j}^* - f_{j^*}}$

References