圈圈学论文（二）区间灰数案例应用

　　分享兴趣，传播快乐，
　　增长见闻，留下美好！
　　亲爱的您，这里是LearningYard学苑。
　　前面小编已经对灰数概念及相关其运算做了详细的讲解，忘记了的同学赶紧复习一下.
　　本节将通过一个实例来显示所提出的区间灰数方法的使用，这可以被视为EGN的一个特例。为了证明所提出的方法具有区间灰数，考虑投资决策公司的评估问题。
　　案例：一家投资银行计划投资三家公司，编号为a1，a2,a3。考虑三个标准：c1，年度产品收入；c2，社会效益；c3，环境污染程度。标准的权重向量表示为W=(0.1,0.2,0.7)。所有三家公司都有三种可能的状态：良好，θ1;普通，θ2；较差,θ3。每个状态的概率表示为区间概率，其中P1=[0.3,0.5],P2=[0.4,0.9.P3=[0.1,0.5]。各方案的标准值采用区间灰数形式，灰色随机变量服从正态分布。
　　下表列出了相关的评估值。可以根据提供的信息选择最佳替代方案。以下程序产生最理想的替代方案。
　　★ 步骤1：规范化决策矩阵。
　　在所给案例中，c1和c2为极大型指标，而c3为极小型指标。应用以下两个等式产生归一化决策矩阵。
　　得到规范化矩阵如下表所示：
　　★步骤2：确定理想点
　　将以下公式应用于规范化矩阵中所示数据，得出绝对理想点I：
　　★步骤3：计算与标准相关的效用值和后悔值
　　计算与标准相关的效用值和后悔值需要考虑两个参数，即风险厌恶系数和后悔厌恶系数。此文中，风险规避系数取值为0.88。假设后悔厌恶系数为0.3。与标准相关的效用值和后悔值可使用上期推文中相关等式确定。
　　★ 步骤4：计算备选方案的总体感知效用值
　　通过应用以下公式：
　　可将上述计算的效用值和后悔值相加，以获得备选方案的感知效用值，如下表所示：
　　下表为计算的整体感知效用值：
　　★步骤5：根据总体感知效用间隔对备选方案进行优先级排序
　　首先，确定总体感知效用区间的正理想解和负理想解：
　　接下来，计算每个总体感知效用区间与正理想解和负理想解之间的距离。
　　最后，获得相对接近度：
　　可以看出C3>C2>C1，因此，确定最佳替代方案为3。下表显示了使用不同值的相对接近度和排名结果。当使用不同的值时，排名结果保持不变。然而，在某些情况下，排名结果可能会随着参数的变化而变化。
　　★英文学习
　　The previous small editor has made a detailed explanation of the concept of gray number and related operations, forgotten students hastened to review, portal:
　　This section will show the use of the proposed interval grays method through an example, which can be considered a special case of EGNs. In order to prove that the proposed method has the interval gray number, consider the evaluation of investment decision-making companies.
　　Case: An investment bank plans to invest in three companies under the numbers a1, a2, a3. Consider three criteria: c1, annual product income; The standard weight vector is represented as W -(0.1,0.2,0.7). All three companies have three possible states: Good, 1; Normal, s2; The probability of each state is expressed as the probability of the interval, where P1 is 0.3, 0.5, P2 is 0.4, 0.9.P3, and 0.1, 0.5. The standard values of each scheme are in the form of interval gray numbers, and the gray random variables obey the normal distribution.
　　The following table lists the relevant evaluation values. The best alternative can be selected based on the information provided. The following procedure produces the ideal alternative.
　　Step 1: Normalize the decision matrix. In the given case, c1 and c2 are very large indicators, while c3 is very small indicators. The following two equations are applied to produce a normalized decision matrix
　　The normalized matrix is shown in the following table:
　　Step 2: Determine the ideal point. Apply the following formula to the data shown in the normalization matrix to arrive at the absolute ideal point I:
　　Step 3: Calculate the utility and regret values associated with the standard.
　　Calculating the utility and regret values associated with the standard requires two parameters, namely, the risk aversion factor and the regret aversion factor. In this paper, the risk aversion coefficient is valued at 0.88. Suppose the regret aversion factor is 0.3. The utility and regret values associated with the standard can be determined using the relevant equation in the previous tweet.
　　Step 4: Calculate the overall perceived utility value of the alternative. By applying the following formula:
　　The utility and regret values of the above calculations can be added together to obtain the perceived utility values for the alternative, as shown in the following table:
　　The following table is the calculated overall perceived utility value:
　　Step 5: Prioritize alternatives based on overall perceived utility intervals. First, determine the positive and negative ideal solutions for the overall perceived utility interval:
　　Next, calculate the distance between each overall perceived utility interval and the positive and negative ideal solutions.
　　Finally, get a relative closeness:
　　As can be seen> C3 > C1, therefore, the best alternative is determined to be 3.
　　The following table shows the relative proximity and ranking results of using different values. When different values are used, the ranking result remains the same. However, in some cases, ranking results may vary with parameters.
　　英文翻译：谷歌翻译
　　参考资料：
　　[1]Zhou H , Wang J Q , Zhang H Y . Grey stochastic multi-criteria decision making based on regret theory and TOPSIS[J]. International Journal of Machine Learning and Cybernetics, 2015, 8(2):1-14.
　　本文由LearningYard学苑原创，如有侵权请联系删除。