圈圈学论文（四）：灰关联TOPSIS决策案例分析

灰关联TOPSIS决策案例分析

上期内容呢小编已经对灰关联TOPSIS决策方法的步骤进行了详细的介绍，本期小编将以具体的案例验证所提方法的合理性和客观性，并对结果进行对比分析。

案例介绍

为了对某区域内的5个大型产业的创新能力进行评价，从产业从业者、管理者和相关产业部门聘请专家，得出的评价结果如下表所示：

设5个大型产业分别作为决策评价方案构成方案集A={A1，A2，A3，A4，A5}，五个决策评价指标由左至右分别设为C1，C2，C3，C4，C5，构成属性集C，方案Ai在Cj下的指标值如下所示，所有指标值构成决策矩阵X。

决策过程

步骤1:对矩阵X进行规范化处理，得出的规范化决策矩阵Y如表3-2所示，接着，求出矩阵Y的正负理想方案决策向量，分别为：

步骤2：求出矩阵Y中各决策属性值的正优势度和负优势度，并构建出正负优势度矩阵S+和S-，如以下两个表所示：

步骤3：对于决策属性权重，根据文献已给出的指标权重向量，代入优化模型，进一步进行优化调整。运用Lingo11.0对模型进行求解，参数决策值正优势度所占重要程度取值0.5，客观权重的重要程度取值0.5，得出的属性综合权重向量w为：

步骤4：由关联度计算公式求出各决策方案的综合关联度，分别为：

根据以上计算结果，方案的优劣排序为A4>A2>A5>A3>A1，由此可以得出创新能力最强的产业为A4，五个产业的创新能力强弱顺序为：A4>A2>A5>A3>A1。

对比分析

通过对评价结果进行分析。产业A4的综合关联度远高于其他产业，因此应将产业A4作为其他产业的创新示范性产业；而经过对综合关联度的分析，可以将五个大型产业的创新能力分为4个层次，第一层次为产业A4，第二层次为产业A2和产业A5，第三层次为产业A3，而第四层次为产业A1，所有低层次标号的产业都应向高层次标号的产业学习；进一步通过正负优势度矩阵从评价指标上对产业的创新能力进行分析，可以发现，第二层次的产业需要在科研基础和制度完善度方面予以加强；第三层次的产业在经济基础指标上表现较差，因此应加强经济基础方面的建设；而第四层次的产业则需要在各方面进行加强。

英文学习

Case introduction: In order to evaluate the innovation ability of 5 large industries in a certain region, experts are hired from industry practitioners, managers and related industry departments, and the evaluation results obtained are shown in the following table:

Suppose 5 large-scale industries are respectively used as the decision-making evaluation program composition program set A={A1, A2, A3, A4, A5}, and the five decision-making evaluation indicators are respectively set as C1, C2, C3, C4, C5 from left to right, which constitute Attribute set C, the index values of scheme Ai under Cj are as follows, and all index values constitute the decision matrix X.

Decision-making process:

Step 1: Normalize the matrix X, and the resulting standardized decision matrix Y is shown in Table 3-2. Next, calculate the positive and negative ideal solution decision vectors of the matrix Y, which are respectively

Step 2: Calculate the positive dominance and negative dominance of each decision attribute value in matrix Y, and construct the positive and negative dominance matrices S+ and S-, as shown in Table 3-3 and Table 3-4;

Step 3: Regarding the decision attribute weight, according to the index weight vector given in the literature, it is substituted into the optimization model to further optimize and adjust. Using Lingo11.0 to solve the model, the importance of the positive dominance of the parameter decision value is 0.5, and the importance of the objective weight is 0.5. The resulting attribute comprehensive weight vector w is:

Step 4: Calculate the comprehensive correlation degree of each decision-making scheme from the correlation degree calculation formula, which are:

Based on the above calculation results, the ranking of the schemes is A4>A2>A5>A3>A1. It can be concluded that the industry with the strongest innovation ability is A4, and the order of the innovation ability of the five industries is: A4>A2> A5>A3>A1.

Comparative analysis: by analyzing the evaluation results. The comprehensive relevance of industry A4 is much higher than that of other industries. Therefore, industry A4 should be regarded as an innovative demonstration industry for other industries. After analyzing the comprehensive relevance, the innovation capabilities of five large industries can be pided into 4 levels. The first level is industry A4, the second level is industry A2 and industry A5, the third level is industry A3, and the fourth level is industry A1. All low-level labeled industries should learn from high-level labeled industries; further pass The positive and negative advantage degree matrix analyzes the innovation ability of the industry from the evaluation indicators, and it can be found that the second-tier industries need to be strengthened in terms of scientific research foundation and institutional perfection; the third-tier industries perform poorly on economic basic indicators Therefore, the construction of the economic foundation should be strengthened; and the fourth-level industry needs to be strengthened in all aspects.

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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