topsis法是什么方法（​TOPSIS简介与例题分析）

1.TOPSIS法定义

TOPSIS （Technique for Order Preference by Similarity to an Ideal Solution ）法是C.L.Hwang和K.Yoon于1981年首次提出，TOPSIS法根据有限个评价对象与理想化目标的接近程度进行排序的方法，是在现有的对象中进行相对优劣的评价。TOPSIS法是一种逼近于理想解的排序法，该方法只要求各效用函数具有单调递增（或递减）性就行。TOPSIS法是多目标决策分析中一种常用的有效方法，又称为优劣解距离法。

The TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method was first proposed by CLHwang and K. Yoon in 1981. The TOPSIS method ranks according to the closeness of a limited number of evaluation objects to the idealized target. The relative pros and cons of the objects are evaluated. The TOPSIS method is a sorting method that approximates the ideal solution. The method only requires that each utility function has a monotonic increase (or decrease). TOPSIS method is a commonly used effective method in multi-objective decision analysis, and it is also called the distance method of superior and inferior solutions.

2.TOPSIS法简介

TOPSIS法是一种理想目标相似性的顺序选优技术,在多目标决策分析中是一种非常有效的方法。它通过归一化后的数据规范化矩阵,找出多个目标中最优目标和最劣目标(分别用理想解和反理想解表示) ,分别计算各评价目标与理想解和反理想解的距离,获得各目标与理想解的贴近度,按理想解贴近度的大小排序,以此作为评价目标优劣的依据。贴近度取值在0～1 之间,该值愈接近1,表示相应的评价目标越接近最优水平;反之,该值愈接近0,表示评价目标越接近最劣水平。该方法已经在土地利用规划、物料选择评估、项目投资、医疗卫生等众多领域得到成功的应用,明显提高了多目标决策分析的科学性、准确性和可操作性。

其基本原理，是通过检测评价对象与最优解、最劣解的距离来进行排序，若评价对象最靠近最优解同时又最远离最劣解，则为最好；否则为最差。其中最优解的各指标值都达到各评价指标的最优值。最劣解的各指标值都达到各评价指标的最差值。

TOPSIS法中“理想解”和“负理想解”是TOPSIS法的两个基本概念。所谓理想解是一设想的最优的解（方案），它的各个属性值都达到各备选方案中的最好的值；而负理想解是一设想的最劣的解（方案），它的各个属性值都达到各备选方案中的最坏的值。方案排序的规则是把各备选方案与理想解和负理想解做比较，若其中有一个方案最接近理想解，而同时又远离负理想解，则该方案是备选方案中最好的方案。

TOPSIS method is a sequential optimization technique based on the similarity of ideal goals, and it is a very effective method in multi-objective decision analysis. It uses the normalized data normalization matrix to find the optimal goal and the worst goal among multiple goals (represented by ideal solutions and anti-ideal solutions), and calculate the distance between each evaluation goal and the ideal solution and the anti-ideal solution. , Obtain the closeness of each target to the ideal solution, sort by the closeness of the ideal solution, and use this as the basis for evaluating the quality of the target. The closeness value is between 0 and 1. The closer the value is to 1, the closer the corresponding evaluation target is to the optimal level; conversely, the closer the value is to 0, the closer the evaluation target is to the worst level. This method has been successfully applied in many fields such as land use planning, material selection evaluation, project investment, medical and health, etc. It has obviously improved the scientificity, accuracy and operability of multi-objective decision analysis.

The basic principle is to sort by detecting the distance between the evaluation object and the optimal solution and the worst solution. If the evaluation object is closest to the optimal solution and farthest from the worst solution, it is the best; otherwise, it is the worst. Each index value of the optimal solution reaches the optimal value of each evaluation index. Each index value of the worst solution reaches the worst value of each evaluation index.

The "ideal solution" and "negative ideal solution" in the TOPSIS method are two basic concepts of the TOPSIS method. The so-called ideal solution is a conceived optimal solution (scheme), each of its attribute values reaches the best value among the alternatives; while a negative ideal solution is a conceived worst solution (scheme), it The attribute values of all reach the worst value among the alternatives. The rule of scheme ordering is to compare each alternative with the ideal solution and the negative ideal solution. If one of the alternatives is closest to the ideal solution and at the same time far away from the negative ideal solution, then it is the best one among the alternatives .

3.TOPSIS法例题

例：评价下列同学身体素质（人体最佳体温36℃~37℃，人体体液pH值最佳范围7.35~7.45）

Example: Evaluate the physical fitness of the following classmates (the best body temperature of the human body is 36°C~37°C, and the best pH value of the body fluid is 7.35~7.45)

第一步：体温指标正向化处理

Step 1: Positive treatment of body temperature indicators

第二步：PH值指标正向化处理

Step 2: Positive processing of the PH value index

第三步：求正向化后的各列元素的平方和和开根号

Step 3: Find the square sum and root sign of each column of elements after normalization

第四步：标准化处理：每个元素除以其所在列各元素平方和的开方

Step 4: Standardization: divide each element by the square root of the sum of the squares of the elements in the column

第五步：求正理想解和负理想解，计算得分

Step 5: Find the positive ideal solution and the negative ideal solution, and calculate the score

第六步：计算得分，得出排名

Step 6: Calculate the score and get the ranking