TOPSIS综合评价

　　01. TOPSIS简介
　　C.L.H wang和K. Yoon于1981年首次提出TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)，可翻译为逼近理想解排序法，国内常简称为优劣解距离法。
　　TOPSIS法是一种常用的综合评价方法，能充分利用原始数据的信息，其结果能精确地反映各评价方案之间的差距。
　　C.L.H wang and K. Yoon first proposed TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) in 1981, which can be translated as a sorting method that approximates an ideal solution. It is often referred to as the distance method between superior and inferior solutions in China.
　　The TOPSIS method is a commonly used comprehensive evaluation method, which can make full use of the information of the original data, and its results can accurately reflect the gap between the evaluation programs.
　　02.算法步骤
　　（1）将原始数据矩阵统一指标类型（一般正向化处理）得到正向化的矩阵；
　　极小型→极大型：
　　(1) Unify the index type of the original data matrix (generally normalized processing) to obtain a normalized matrix;
　　Very small → very large:
　　中间型→极大型：
　　Intermediate type→extremely large:
　　区间型→极大型：
　　Interval type→Extremely large:
　　（2）再对正向化的矩阵进行标准化处理以消除各指标量纲的影响；
　　(2) Standardize the normalized matrix to eliminate the influence of each indicator dimension;
　　（3）并找到有限方案中的最优方案和最劣方案：
　　(3) And find the best plan and the worst plan among the limited plans:
　　（4）然后分别计算各评价对象与最优方案和最劣方案间的距离；
　　(4) Then calculate the distance between each evaluation object and the best and worst solutions;
　　（5）获得各评价对象与最优方案的相对接近程度，以此作为评价优劣的依据。
　　(5) Obtain the relative closeness of each evaluation object to the optimal plan, and use this as the basis for evaluating the pros and cons.
　　03.增加权重
　　如果给各指标赋予权重的话，该如何计算呢？
　　那么赋予权重之后的与最优、最劣方案的距离就变成了：
　　If you attach weights to each indicator, how do you calculate it?
　　Then the distance to the best and worst solutions after attaching the weights becomes:
　　其他步骤依然不变，当然也可以先对标准化矩阵中的每个元素计算权重，然后直接用带权重的标准化矩阵来计算得分，这样得到的结果和在计算距离时引入的权重结果几乎是相同的。
　　The other steps remain the same. Of course, you can first calculate the weight for each element in the standardized matrix, and then directly use the standardized matrix with weight to calculate the score, so that the result obtained is almost the same as the result of the weight introduced when calculating the distance. .
　　参考资料：CSDN、谷歌翻译
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