Why does the video say the entropy method does not need pairwise comparison opinions like AHP?

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.

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.