周四学习卡——熵权法

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分享兴趣，传播快乐，增长见闻，留下美好！亲爱的您，这里是LearningYard学苑。常用的计算权重的方法可以分为主观赋权法和客观赋权法两类，主观赋权法包括德尔菲法和层次分析法，常用的客观赋权法有：因子分析法、主成分分析法、神经网络法、熵权法等。今天小编将带领大家了解客观赋权法中的熵权法，一起来看看吧！

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1.基本概念

熵是指系统的混乱程度，熵的概念最早是由德国物理学家鲁道夫•克劳修于1850年提出，并首先应用于热力学中。克劳德•艾尔伍德•香农第一次将熵的概念引入到信息论中，用它来衡量信息的不确定性，由此开始熵的概念在信息论中得到了广泛的应用。

Entropy refers to the degree of chaos in a system. The concept of entropy was first proposed by the German physicist Rudolf Clausius in 1850, and was first applied to thermodynamics. Claude Elwood Shannon introduced the concept of entropy into information theory for the first time, and used it to measure the uncertainty of information. Since then, the concept of entropy has been widely used in information theory.

依据信息熵的概念，信息熵可以用于对信息量变异程度的确定：一般来说信息系统越有序，其信息熵值越低；如果一个信息系统越混乱，则信息熵值越高。

According to the concept of information entropy, information entropy can be used to determine the degree of variation in the amount of information: Generally speaking, the more orderly an information system is, the lower its information entropy value; if an information system is more chaotic, the higher the information entropy value.

熵权法就是依据了信息熵的这个特点，运用评价指标的变化程度来确定该指标在整个评价体系中所占的权重。如果某个评价指标的变化程度越大，那么该指标就具有越大的信息量，也就是说该指标在评价体系中所占的权重也就越大；反之亦然。

The entropy weight method is based on this characteristic of information entropy, and uses the degree of change of the evaluation index to determine the weight of the index in the entire evaluation system. If the degree of change of an evaluation index is greater, the index has a greater amount of information, that is to say, the weight of the index in the evaluation system is greater; and vice versa.

2.计算过程

①假设指标体系包含m个样本，n项指标，那么原始矩阵为：

①Assuming that the indicator system contains m samples and n indicators, then the original matrix is:

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②对指标进行标准化处理。为了避免指标的量纲以及量纲单位不一致的问题，需要对各指标采取标准化处理的措施。正向指标的标准化处理：

② Standardize the indicators. In order to avoid the inconsistency of the dimensions of the indicators and the units of the dimensions, it is necessary to take standardized measures for each indicator. Standardization of positive indicators:

​

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负向指标的标准化处理：

Standardization of negative indicators:

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③原始矩阵R的标准化，表示为

③ Standardization of the original matrix R, expressed as

​

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其中Pij表示权重，其公式为

where Pij represents the weight, and its formula is

​

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④熵的表达。定义指标i的熵值，其公式为：

④ the expression of entropy. Define the entropy value of the index i, and its formula is:

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⑤计算第i个指标的熵权Ui，其公式为：

Calculate the entropy weight Ui of the ith index, and its formula is:

​

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3.优缺点

优点：

熵权法计算权重的过程需要判定每个数值所涵盖的信息量，避免了专家评审带来的非客观性，计算结果精度较高，能够更加严密地解释所得到的结果。

Advantage:

The process of calculating the weight by the entropy weight method needs to determine the amount of information covered by each value, which avoids the non-objectivity caused by the expert review, and the calculation results are more accurate and can more closely interpret the obtained results.

缺点：

①由于熵权法的计算完全依托于指标数值，对于指标与指标之间的联系可能造成忽略；

②熵权法在计算过程中对指标没有筛选，无法像因子分析法和主成分分析法一样计算其中对于分析结果贡献率最大的指标；

③当各项指标的变动差异很小时，熵权法的计算受到限制。

Shortcoming:

① Since the calculation of the entropy weight method completely relies on the index value, the relationship between the index and the index may be ignored;

② The entropy weight method does not screen the indicators in the calculation process, and cannot calculate the indicators with the largest contribution rate to the analysis results like the factor analysis method and the principal component analysis method;

③ When the variation difference of each index is very small, the calculation of entropy weight method is limited.

英文翻译：谷歌翻译；

参考资料：

[1]周师兄学习文档；

[2]乔吴清. 基于熵权法TOPSIS模型的好想你食品公司O2O转型财务绩效评价研究[D].

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