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上期内容呢小编对灰关联聚类决策做了简单的介绍，本期将通过具体案例对灰关联聚类决策的步骤进行详细说明。

案例介绍

本案例将从技术、管理、财政、企业家素质和企业文化五个方面对民营企业进行评估，对8家民营企业进行评级并进一步选出核心竞争力最强的民营企业。8家民营企业将被划分为三个类别：核心竞争力强、一般和弱。8家企业各指标分数如下表所示：

接着确定各指标下的可能度函数，由于本方法中的灰关联聚类分析是在对原始数据规范化处理后进行的，因此也需要对可能度函数进行规范化处理，使其取值范围在[0，1]之间。处理后的可能度函数性质不变，并适用于灰关联聚类决策方法，具体如下：

技术能力指标的三类可能度函数为：

管理能力指标的三类可能度函数为：

财务能力指标的三类可能度函数为：

企业家素质指标的三类可能度函数为：

企业文化指标的三类可能度函数为：

决策过程

步骤1：

对表中样本矩阵进行规范化处理，得到的无量纲化决策矩阵下表所示：

步骤2：

经计算，理想最优决策向量和临界决策向量分别为：

进一步求出各个公司的各指标值关于相应的理想方案决策值和临界方案决策值之间的灰色区间关联系数，

根据灰色综合区间关联系数公式：

进一步求出各决策属性值的灰色综合区间关联系数，构成系数矩阵，结果如下：

步骤3：

根据公式：

求出各指标的权重，得出的指标权重向量为：

步骤4：

将灰关联系数矩阵代入到给出的可能度函数当中，结合权重向量w，进行聚类分析，得出8家企业所属灰类的聚类系数，分别为：

从结果可以看出，企业1、2、3属于第二类，即核心竞争力一般；企业4、5、6、7、8属于第三类，即核心竞争力较弱。

英文学习

In the last issue, the editor gave a brief introduction to grey relational clustering decision-making. In this issue, the steps of grey relational clustering decision-making will be explained in detail through specific cases.

Case background:

Private enterprises were evaluated from five aspects: technology, management, finance, entrepreneurial quality, and corporate culture. Eight private enterprises were rated and the private enterprises with the strongest core competitiveness were further selected. The 8 private enterprises will be divided into three categories: strong core competitiveness, average and weak. The scores of each indicator of the 8 companies are shown in the following table:

Then determine the probability function under each indicator. Because the gray relational clustering analysis in this method is performed after the original data is normalized, it is also necessary to normalize the probability function so that its value range is [0 , 1] between. The nature of the probability function after processing remains unchanged, and it is suitable for grey relational clustering decision-making method, as follows:

The three possible degree functions of technical capability indicators are:

The three possible degree functions of management capability indicators are:

The three possible degree functions of financial capability indicators are:

The three possible degree functions of entrepreneur quality indicators are:

The three possible degree functions of corporate culture indicators are:

Steps

step 1:

After normalizing the sample matrix in the table, the dimensionless decision matrix obtained is shown in the following table:

Step 2: After calculation, the ideal optimal decision vector and the critical decision vector are respectively

Further calculate the gray interval correlation coefficients between the corresponding ideal plan decision value and the critical plan decision value of each index value of each company,

According to the gray comprehensive interval correlation coefficient formula:

Further calculate the gray comprehensive interval correlation coefficient of each decision attribute value to form a coefficient matrix, and the results are as follows

Step 3: According to the formula:

Calculate the weight of each indicator, and the obtained indicator weight vector is:

Step 4: Substitute the gray correlation coefficient matrix into the given possibility function, combine the weight vector w, perform cluster analysis, and obtain the cluster coefficients of the gray categories of the 8 companies, which are:

It can be seen from the results that enterprises 1, 2, and 3 belong to the second category, that is, the core competitiveness is average; enterprises 4, 5, 6, 7, and 8 belong to the third category, that is, the core competitiveness is weak.

英文翻译：谷歌翻译

参考资料：

[1]牛玉飞. 三参数区间灰数信息下的多属性决策方法研究[D].河南农业大学,2018.

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