Decision.EntropyWeights

This function calculates the weights of decision criteria using the entropy weighting method. It analyzes the distribution of values across each criterion to determine their relative importance based on information entropy.

Syntax

Decision.EntropyWeights(
    tbl as table,
    optional columnNames as {text}
) as record

Parameters

• tbl: The input table containing numeric values for each criterion.
• columnNames (optional): A list of column names to include in the calculation. If not provided, all numeric columns in the table will be used.

Remarks

• The entropy weighting method is a data-driven approach to determine the importance of each criterion based on its variability.
• The function performs the following steps:
  • Normalization of each criterion using min-max scaling.
  • Calculation of entropy for each criterion based on the normalized values.
  • Computation of weights:
    • $w_{j}=\frac{1−s_{j}}{m−\sum_{j=1}^{m}{s_{j}}}​$
  • where:
    • $s_j$​ is the entropy of criterion $j$,
    • $m$ is the number of criteria.
• If all values in a column are equal, its entropy is the maximum and its weight is zero.
• If the table has only one row, all criteria receive equal weight.

Return Value

Returns a record where each field name corresponds to a criterion and each field value is the calculated weight.

Examples

Example 1: Entropy weights for all numeric columns. Weights are assigned based on the variability of each criterion.

let
    Source = #table(type table
        [Cost=number, Quality=number, Speed=number], {
        {300, 80, 60},
        {250, 70, 75},
        {400, 90, 50}
    }),
    Result = Decision.EntropyWeights(Source)
in
    Result

Result

[Cost = 0.36, Quality = 0.31, Speed = 0.33]

Example 2: Calculates entropy weights only for specified columns.

let
    Source = #table(type table
        [Cost=number, Quality=number, Speed=number], {
        {300, 80, 60},
        {250, 70, 75},
        {400, 90, 50}
    }),
    Result = Decision.EntropyWeights(Source, {"Cost", "Speed"})
in
    Result

Result

[Cost = 0.52, Speed = 0.48]