vikor
mcda.vikor
VIKOR aggregation: rank tools by a compromise between group utility and individual regret.
Functions
| Name | Description |
|---|---|
| vikor | Compute VIKOR compromise scores per tool. |
vikor
mcda.vikor.vikor(normalized, weights, v=0.5)
Compute VIKOR compromise scores per tool.
VIKOR (Opricovic 1998; Opricovic and Tzeng 2004) ranks tools by how close they sit to an ideal solution, balancing two views. The group utility S is the weighted Manhattan distance from the ideal, so it rewards a tool that does well summed across all metrics. The individual regret R is the weighted Chebyshev distance, so it penalizes a tool’s single worst metric. The compromise index Q blends the two:
Q_i = v * (S_i - S_star) / (S_minus - S_star)
+ (1 - v) * (R_i - R_star) / (R_minus - R_star)where S_star and R_star are the column minima of S and R, S_minus and R_minus their maxima, and v in [0, 1] weights group utility against regret. With v = 1 the index follows S alone (majority rule, maximum group utility); with v = 0 it follows R alone (minimum individual regret); v = 0.5 is the usual consensus default.
The input is already normalized to [0, 1] with every column oriented so higher is better, so per metric the best value f_star is the column max and the worst f_minus is the column min. The per-criterion distance for tool i on metric j is
d_ij = (f_star_j - x_ij) / (f_star_j - f_minus_j)weighted by the metric weight. A criterion with zero range (f_star == f_minus) carries no information between tools and contributes nothing.
The compromise index Q is computed by pymcdm.methods.VIKOR with its normalization disabled, so pymcdm runs on beam’s already normalized matrix. The native S, R and Q loop has been replaced by that call.
Orientation convention. The canonical VIKOR Q is lower is better: the tool with the smallest Q is the preferred compromise. beam aggregations must return a higher-is-better preference score so that beam.mcda.rank (1 = highest score) gives the ranking. This function therefore returns -Q. Negating preserves the order exactly: the tool with the smallest Q has the largest -Q and so ranks first. We return -Q rather than a rescaled 1 - Q to avoid a second normalization step that would discard the absolute spacing of the Q values.
Degenerate cases are guarded. If every tool is identical on a metric the column range is zero and that metric carries no information. pymcdm rejects a constant column, so beam drops such columns before the call. When every column is constant, which happens for a single tool or for rows identical on every metric, there is nothing to separate the tools, so beam returns a constant score and leaves all tools tied.
Parameters
| Name | Type | Description | Default |
|---|---|---|---|
normalized |
np.ndarray | Shape (n_tools, n_metrics), values in [0, 1], higher is better. |
required |
weights |
np.ndarray | Shape (n_metrics,), non-negative; typically sums to 1. |
required |
v |
float | Compromise parameter in [0, 1]. Weight on group utility S versus individual regret R. Default 0.5. | 0.5 |
Returns
| Type | Description |
|---|---|
| np.ndarray | Shape (n_tools,), the higher-is-better preference score -Q. |
References
Opricovic, S. Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade (1998).
Opricovic, S. and Tzeng, G.-H. Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research 156(2), 445-455 (2004).