圈圈学论文（五）灰关联聚类决策

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　　亲爱的您，这里是LearningYard学苑。今天小编给大家带来的决策方法制灰关联聚类决策。
　　CHAPTER 01
　　1.方法简介
　　灰关联分析和灰聚类分析作为灰色系统理论中两种重要的系统分析方法，目前已有广泛的研究，而灰关联聚类结合灰关联和聚类方法的优点，作为一种新的系统分析方法正越来越多的地运用于多属性决策当中。
　　本文提出的灰关联聚类决策方法则同时运用了灰关联和灰聚类的分析方法，使聚类结果更加符合决策数据为三参数区间灰数的特点；为综合考虑各方案与理想最优方案和临界方案两者的关联关系，运用综合区间关联系数来表示各决策值的优劣程度，提高聚类结果的准确性。并且在已给出的灰关联聚类决策方法的基础上，通过引入后悔理论，计算出各决策对象关于各指标的灰关联综合感知效用值，再将其代入到灰色聚类的可能度函数当中进行灰色聚类分析，实现了后悔理论与灰关联聚类方法的有机结合。
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　　CHAPTER 02
　　2.问题描述
　　本文的问题可以简单描述为：依据各个方案原始决策信息和各灰类关于各属性的可能度函数，确定各决策方案所属灰类，并进一步确定在同一灰类中各个方案的排序结果。
　　所有决策效果向量构成方案决策矩阵D：
　　现有灰类集Y={y1，y2，…y}，方案ai（i=1，2…，n）关于属性cj（j=1，2…，m）且属于灰类yk（k=1，2…，s）的可能度函数，根据不同灰类确定其属于何种类型的可能度函数。
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　　CHAPTER 03
　　3.决策步骤
　　步骤1 ：根据决策样本矩阵D，对属性值进行规范化处理，得到无量纲化矩阵X；
　　步骤2 ：求出出理想方案决策向量和临界方案决策向量，再分别求出决策值关于理想方案子因素和临界方案子因素的灰关联系数，并得出Y+和Y-，进一步求出灰色区间综合关联系数；
　　步骤3 ：求出各决策属性权重；
　　步骤4 ：求出综合区间关联系数的感知效用值，再分别求出欣喜值和后悔值，进一步出各指标值的灰关联综合感知效用，，并构建矩阵U；
　　步骤5 ：对决策方案进行灰色定权聚类，得出各方案所属灰类，并在类内实现方案排序。
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　　CHAPTER 04
　　英文学习
　　Grey relational analysis and grey clustering analysis, as two important system analysis methods in grey system theory, have been extensively studied at present, and grey relational clustering combines the advantages of grey relational and clustering methods as a new system analysis Methods are increasingly being used in multi-attribute decision making.
　　The grey relational clustering decision-making method proposed in this paper uses both grey relational and grey clustering analysis methods to make the clustering result more consistent with the characteristics of the decision data as a three-parameter interval grey number; to comprehensively consider each plan and the ideal optimal plan For the correlation between the two and the critical scheme, the comprehensive interval correlation coefficient is used to indicate the pros and cons of each decision value, and the accuracy of the clustering results is improved. And on the basis of the gray correlation clustering decision-making method that has been given, through the introduction of regret theory, the gray correlation comprehensive perceived utility value of each decision object with respect to each index is calculated, and then it is substituted into the gray clustering possibility function. The grey clustering analysis has realized the organic combination of regret theory and grey relational clustering method.
　　Problem Description:
　　The problem in this paper can be simply described as: According to the original decision information of each plan and the possibility function of each gray class on each attribute, determine the gray class of each decision plan, and further determine the ranking result of each plan in the same gray class.
　　All decision-making effect vectors constitute the scheme decision matrix D:
　　The existing gray class set Y={y1, y2,...y}, the scheme ai (i=1, 2..., n) is about the attribute cj (j=1, 2..., m) and belongs to the gray class yk (k=1 , 2..., s) possibility degree function, according to different gray classes to determine which type of possibility degree function it belongs to.
　　Decision steps:
　　Step 1: According to the decision sample matrix D, normalize the attribute value to obtain the dimensionless matrix X;
　　Step 2: Calculate the ideal plan decision vector and the critical plan decision vector, and then respectively calculate the gray correlation coefficients of the decision value on the ideal plan sub-factors and the critical plan sub-factors, and get Y+ and Y-, and further calculate the gray interval Comprehensive correlation coefficient;
　　Step 3: Calculate the weight of each decision attribute;
　　Step 4: Calculate the perceived utility value of the comprehensive interval correlation coefficient, then calculate the joy value and regret value respectively, and further calculate the gray correlation comprehensive perceived utility of each index value, and construct the matrix U;
　　Step 5: Perform grey fixed weight clustering on the decision-making schemes, obtain the gray class of each scheme, and realize the ordering of schemes within the class.
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　　英文翻译：谷歌翻译
　　参考文献：[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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