pymcdm.distances

pymcdm.distances.draWS(x, y)

Calculate drastic WS distance between the ranking vectors [1]. Rankings should be presented as indices, i.e. for the ranking A2 > A1 > A3 the ranking vector should be [2, 1, 3].

Parameters:

• x (ndarray | list | tuple) – First vector of ranks.

• y (ndarray | list | tuple) – Second vector of ranks.

Returns:

Drastic distance between two rankings vectors.

Return type:

float

References

[1]

Sałabun, W., & Shekhovtsov, A. (2023, September). An innovative drastic metric for ranking similarity in decision-making problems. In 2023 18th Conference on Computer Science and Intelligence Systems (FedCSIS) (pp. 731-738). IEEE.

pymcdm.distances.frobenius(r1, r2)

Calculate Frobenius distance between two ranking vectors [2]. Rankings should be presented as indices, i.e. for the given objects [A1, A2, A3] and ordering A2 > A1 > A3, the ranking vector should be [2, 1, 3].

Parameters:

• r1 (ndarray | list | tuple) – First ranking vector in indices format.

• r2 (ndarray | list | tuple) – Second ranking vector in indices format.

Returns:

Frobenius distance between two ranking vectors.

Return type:

float

References

[2]

Dezert, J., Shekhovtsov, A., & Sałabun, W. (2024). A new distance between rankings. Heliyon, 10(7).

pymcdm.distances.kemeny(r1, r2)

Calculate Kemeny distance between two ranking vectors [3]. Rankings should be presented as indices, i.e. for the given objects [A1, A2, A3] and ordering A2 > A1 > A3, the ranking vector should be [2, 1, 3].

Parameters:

• r1 (ndarray | list | tuple) – First ranking vector in indices format.

• r2 (ndarray | list | tuple) – Second ranking vector in indices format.

Returns:

Kemeny distance between two ranking vectors.

Return type:

float

References

[3]

Kemeny, J. G. (1959). Mathematics without numbers. Daedalus, 88(4), 577-591.