VIKOR算法简介及步骤

　　VIKOR法简介：
　　Opricovic于1998年提出了VIKOR决策方法，它是一种折衷排序方法，通过最大化群效用和最小化个体遗憾值对有限决策方案进行折衷排序。VIKOR方法是多准则决策（MCDM）的有效工具，用于以下情形：
　　（1）决策者不能或不知道如何准确表达其偏好；
　　（2）评价准则间存在冲突和不可公度（测度单位不同）；
　　（3）处理冲突问题的决策者能够接受妥协解方案。
　　VIKOR方法的基本上思想是：确定正理想解（PIS）与负理想解（NIS），然后比较待选方案的评估值，根据其于理想指标值的距离大小择优。其中，正理想解是各评价准则中的最优值，而负理想解则是各评价准则中的最差值。
　　VIKOR方法基于以下形式的测度：
　　Opricovic proposed the VIKOR decision-making method in 1998, which is a compromise ranking method, which compromises and ranks limited decision-making schemes by maximizing group utility and minimizing inpidual regret values. The VIKOR method is an effective tool for multi-criteria decision-making (MCDM), used in the following situations:
　　(1) Decision makers cannot or do not know how to accurately express their preferences;
　　(2) There are conflicts and incommensurability among the evaluation criteria (different measurement units);
　　(3) Decision makers dealing with conflict issues can accept compromise solutions.
　　The basic idea of the VIKOR method is to determine the positive ideal solution (PIS) and the negative ideal solution (NIS), and then compare the evaluation values of the options to be selected, and choose the best according to the distance from the ideal index value. Among them, the positive ideal solution is the optimal value in each evaluation criterion, and the negative ideal solution is the worst value in each evaluation criterion.
　　The VIKOR method is based on measures of the following form:
　　算法步骤
　　（1）模型构建（以实数为例）
　　(1) Model construction (take real numbers as an example)
　　（2）决策指标标准化
　　标准化处理是为了消除量纲对最终结果的影响，使不同变量具有可比性。决策指标包含效益型指标和成本型指标。效益型指标是正向化指标，数值越大表示决策者对该项越满意；成本型指标属于负向化指标，其数值越大决策者对该指标的满意度越低。
　　标准化处理公式：
　　(2) Standardization of decision-making indicators
　　Standardization is to eliminate the influence of dimensions on the final result and make different variables comparable. Decision-making indicators include benefit-type indicators and cost-type indicators. The benefit index is a positive index. The larger the value, the more satisfied the decision maker is with the item; the cost index belongs to the negative index. The larger the value, the lower the decision maker’s satisfaction with the index.
　　Standardized processing formula:
　　（3）确定群体效用与个体遗憾
　　(3) Determine group utility and inpidual regret
　　（4）计算折衷决策指标值
　　根据群体效用值与个体遗憾值的结果，在此基础上计算决策指标的值，指标值越小方案越优。
　　(4) Calculate the value of compromise decision index
　　According to the results of the group utility value and the inpidual regret value, the value of the decision-making index is calculated on this basis. The smaller the index value, the better the solution.
　　最终，可以得到各方案的指标值，而指标值越小越好，将指标进行升序排列得到各方案的排序结果。
　　In the end, the index value of each program can be obtained, and the smaller the index value is, the better. Sort the indexes in ascending order to get the sorting result of each program.
　　（5）确定备选方案排序及折衷方案
　　(5) Determine the ranking of alternative plans and compromise plans
　　参考资料：谷歌翻译
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