What does entropy weight mean in multi-criteria decision making?

You calculate the final objective weights $w_j$ by normalizing the degree of diversification. The formula is $w_j = \frac{1 - e_j}{\sum_{j=1}^n (1 - e_j)}$, which divides each criterion's degree of diversification by the sum of all degrees of diversification.

Conditions: The entropy values $e_j$ have been calculated for all criteria.; The sum of all degrees of diversification is nonzero.

The entropy values for the four criteria are $e_1=0.99375$ for Price or Cost, $e_2=0.96296$ for Storage Space, $e_3=0.97185$ for Camera, and $e_4=0.97367$ for Looks.

Conditions: The example uses 5 alternatives and 4 criteria.; The scaling constant $h$ is 0.621335.; The matrix has been normalized prior to calculation.

The entropy formula is $e_j=-h\sum_{i=1}^{m}r_{ij}\ln r_{ij}$. The constant $h$ is a scaling factor defined as $1/\ln(m)$, where $m$ is the number of alternatives, ensuring the entropy values are properly scaled.

Conditions: The decision matrix has already been normalized to produce $r_{ij}$.; The natural logarithm $\ln$ is used.; $m$ represents the total number of alternatives (rows).

The degree of diversification, denoted as $d_j$, is defined as $1 - e_j$. It represents the amount of useful information or distinguishing power provided by a specific criterion among the alternatives.

Conditions: The entropy value $e_j$ has already been calculated for the criterion.; The degree of diversification is always a positive real number in this context.

The entropy method derives weights directly from the data pattern itself, measuring the dispersion of alternatives. Unlike AHP, which requires subjective pairwise comparison judgments from decision makers, the entropy method is objective and data-driven.

Conditions: Comparing the entropy method with the Analytic Hierarchy Process (AHP).; The decision matrix contains the necessary numerical data.