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Answers for “为什么视频说熵方法不需要像层次分析法(AHP)那样的成对比较意见?”

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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.

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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.

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You calculate the final objective weights wjw_j by normalizing the degree of diversification. The formula is wj=1−ej∑j=1n(1−ej)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 eje_j have been calculated for all criteria.; The sum of all degrees of diversification is nonzero.

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You normalize the decision matrix by dividing each entry by the sum of its own column. This column-wise operation ensures that the sum of the normalized values in each criterion column equals 1.

Conditions: The matrix contains nonnegative numerical attribute values.; The sum of each column must be nonzero.; Normalization is applied independently to each criterion column.

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The degree of diversification, denoted as djd_j, is defined as 1−ej1 - e_j. It represents the amount of useful information or distinguishing power provided by a specific criterion among the alternatives.

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