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今天小编给大家带来期刊论文《属性关联的双极容度多属性决策 VIKOR方法》决策步骤理论基础1，
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Today, the editor brings you the theoretical basis of decision steps in the journal paper "Attribute Association Bipolar Capacity Multi-attribute Decision VIKOR Method" 1,
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在上一期中我们解读了问题描述，接下来让我开始决策步骤的分析学习吧！
In the last issue, we deciphered the problem description, so let's start the analysis and learning of the decision-making steps!
步骤一：确定初始决策矩阵
首先，我们需要根据方案集和属性集确定初始决策矩阵。假设本文中属性关联的多属性决策问题的方案集为A={a1,a2,...,am}，关联的属性集为C={c1,c2,...,cn}。后续的计算需要注意这里的m和n。
Step 1: Determine the initial decision matrix
First, we need to determine the initial decision matrix based on the scenario set and attribute set. Suppose that the solution set of the attribute association multi-attribute decision problem in this article is A={a1,a2,...,am}, and the associated attribute set is C={c1,c2,...,cn}. Subsequent calculations need to pay attention to m and n here.
步骤二：标准化计算
决策表中的数据的规范化有三种作用:
属性值有多种类型。
有些指标的属性值越大越好，如科研成果数、科研经费等是效益型；有些指标的值越小越好，称作成本型。这几类属性放在同一表中不便于直接从数值大小来判断方案的优劣，因此需要对属性表中的数据进行预处理，使表中任一属性下性能越优的值在变换后的属性表中的值越大。
非量纲化。
多目标评估的困难之一是指标间不可公度，即在属性值表中的每一列数具有不同的单位(量纲)。即使对同一属性，采用不同的计量单位，表中的数值也就不同。
归一化。
原属性值表中不同指标的属性值的数值大小差别很大，如总经费即使以万元为单位，其数量级往往在千、万间，为了直观，更为了便于采用各种多目标评估方法进行比较，需要把属性值表中的数值归一化，即把表中数均变换到[0，1]区间上。
因此，本文考虑消除不同属性的物理量纲，需要进行标准化的计算，针对不同类型的属性计算公式不同，具体公式如下所示：
Step 2: Standardize calculations
The normalization of data in decision tables has three functions:
There are several types of property values.
There are several types of property values.
The larger the attribute value of some indicators, the better, such as the number of scientific research achievements, scientific research funds, etc. are efficiency-type; Some indicators have smaller values as much as possible, which is called cost-based. It is not convenient for these types of attributes to directly judge the advantages and disadvantages of the scheme directly from the numerical size in the same table, so the data in the attribute table needs to be preprocessed so that the value with better performance under any attribute in the table will have a larger value in the transformed attribute table.
Non-dimensional.
One of the difficulties of multi-objective evaluation is the inequality between indicators, i.e. the number of columns in the attribute value table has a different unit (dimension). Even if different units of measurement are used for the same attribute, the values in the table are different.
Normalization.
The numerical size of the attribute values of different indicators in the original attribute value table varies greatly, such as the total cost even if it is measured in tens of thousands of yuan, its order of magnitude is often between thousands and thousands, in order to be intuitive, and in order to facilitate the use of various multi-objective evaluation methods for comparison, it is necessary to normalize the values in the attribute value table, that is, to transform the numbers in the table to the [0,1] interval.
Therefore, this paper considers the elimination of physical dimensions of different properties, which needs to be standardized calculations, and the calculation formulas are different for different types of properties, as follows:
步骤三：确定相对距离差矩阵
然后是确定正理想解和负理想解，其中所谓的正理想解指的是备选方案在各评价准则中的最佳值，负理想解备选方案在各评价准则中的最差值。
Step 3: Determine the relative distance difference matrix
This is followed by the determination of positive and negative ideal solutions, where the so-called positive ideal solution refers to the best value of the alternative in the evaluation criteria and the worst value of the negative ideal solution alternative in the evaluation criteria.
根据前景理论，需要确定决策者心理感知的收益和损失，利用如下的前景效用函数计算：
According to the prospect theory, it is necessary to determine the gains and losses of the decision-maker's psychological perception, and use the following prospect utility function calculation:
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参考资料：谷歌翻译、百度百科、知乎
参考文献：
[1]林萍萍,李登峰,江彬倩,余高锋,韦安鹏.属性关联的双极容度多属性决策VIKOR方法[J].系统工程理论与实践,2021,41(08):2147-2156.
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