敏感性分析计算公式（VIKOR算法的敏感性分析及代码实现）

大家晚上好！前面的文章已经详细介绍了VIKOR算法的步骤，忘记了的同学赶紧复习一下！传送门：VIKOR算法简介及步骤

今天就直达主题——VIKOR算法的敏感性分析！所以直接以标准化后的矩阵进行相关操作。

Good evening, everybody! The previous article has introduced the steps of the VIKOR algorithm in detail, and those who forgot to review it quickly! Portal:

Let’s get to the topic today-Sensitivity analysis of VIKOR algorithm! So directly use the standardized matrix to perform related operations.

根据VIKOR折衷决策指标值的公式计算出各方案的Q值分别为：

According to the formula of VIKOR compromise decision index value, the Q value of each scheme is calculated as:

我们将对此结果进行敏感性分析。

We will conduct a sensitivity analysis on this result.

01 决策机制系数扰动

在实际决策中，专家可能有不同的主观决策态度，进而采取不同的折衷系数。如果v>0.5，则表示根据最大化群体效应决策机制决策；如果v<0.5，则表示根据最小化个体遗憾值的决策机制决策；如果v=0.5，则表示根据协商达成最大群体效应和最小个体遗憾值同等重要的决策机制进行决策。随着值的变化，方案排序也会受到影响。

上述结果是将v取0.5进行计算的，因此，接下来将在0~1之间以0.1为步长对v进行11次取值，进行敏感性分析，检验评价模型的稳定性。

代码输入：

In actual decision-making, experts may have different subjective decision-making attitudes, and then adopt different compromise coefficients. If v>0.5, it means that the decision-making mechanism is based on maximizing the group effect; if v<0.5, it means that it is based on the decision-making mechanism that minimizes the individual regret value; if v=0.5, it means that the maximum group effect and the smallest individual are reached through negotiation Regret value is equally important for decision-making mechanisms. As the value changes, the order of the schemes will also be affected.

The above result is calculated by taking v as 0.5. Therefore, the next step will be between 0 and 1 to take the value of v 11 times to conduct sensitivity analysis to test the stability of the evaluation model.

Code input:

输出结果：

Output result:

对扰动后的方案进行排序，输入代码：

To sort the schemes after the disturbance, enter the code:

输出结果：

Output result:

此时我们就可以清晰地看到v取不同的值时个方案的Q值。

At this point, we can clearly see the Q value of the scheme when v takes different values.

02 属性权重扰动

通过敏感性分析,可以确定评价准则权重的潜在变化会导致决策结果产生偏离，这是有效利用模型和实施定量决策的关键。决策中的评价准则权重受到微小扰动后，各潜在供应商优先序的相应变化

将ω以0.05为步长，在[0,2]区间内进行取共41次取值。将权重按照以下公式进行扰动，得到ξ和k。

Through sensitivity analysis, it can be determined that potential changes in the weight of evaluation criteria will lead to deviations in decision-making results, which is the key to effective use of models and implementation of quantitative decision-making. After the weight of the evaluation criteria in the decision-making is slightly disturbed, the priority of each potential supplier changes accordingly

Taking ω as the step size of 0.05, take a total of 41 values in the interval [0,2]. Perturb the weights according to the following formula to obtain ξ and k.

输入代码：

Enter code:

扰动后的结果为164*4的矩阵：

The result after the perturbation is a 164*4 matrix:

根据扰动后的ω矩阵计算新的Q值排序，需要注意的是，代码的开头和结尾有一定变化，中间的代码基本不变。

Calculate the new Q value sorting according to the disturbed ω matrix. It should be noted that there are certain changes at the beginning and end of the code, and the code in the middle is basically unchanged.