How do you calculate the final objective weights using the Entropy Method?

Entropy weight describes how much different alternatives approach one another with respect to a certain criterion. It is a data-driven measure that determines the objective importance of a criterion based on the variability of the data.

Conditions: Applied in multi-criteria decision making contexts.; Weights are derived from the data pattern itself rather than subjective judgments.

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.