萌说新语Matlab入门教程之VIKOR方法

　　Matlab入门教程之VIKOR方法
　　The VIKOR method of Matlab introductory tutorial
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　　The topic that the editor brings to you today is the VIKOR method, and you are welcome to visit with your heart.
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　　一、VIKOR方法简介
　　ntroduction to the VIKOR method
　　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。
　　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.
　　VIKOR方法是多准则决策（MCDM）的有效工具，用于以下情形：
　　（1）决策者无法准确表达其偏好；
　　（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可接受妥协解方案。
　　The VIKOR method is an effective tool for multi-criteria decision-making (MCDM), used in the following situations:
　　(1) Decision makers cannot accurately express their preferences;
　　(2) There are conflicts and incommensurability between evaluation criteria (different measurement units);
　　(3) Decision makers dealing with conflict issues can accept compromise solutions.
　　VIKOR方法的本质
　　The essence of the VIKOR method
　　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。通过最大化群体效益和最小化个体损失得到方案各属性互相让步的折衷妥协解。
　　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. By maximizing group benefits and minimizing inpidual losses, a compromise solution of mutual concessions among the various attributes of the scheme is obtained.
　　VIKROR基于以下形式的Lp测度
　　VIKROR is based on the Lp measure of the following form
　　与TOPSIS相比，VIKOR方法既有前者的正负理想值概念，还具备妥协个体和群体利益的折衷解，更适合解决存在利益冲突的多准则决策问题。
　　Compared with TOPSIS, the VIKOR method not only has the former concept of positive and negative ideal values, but also has a compromise solution that compromises the interests of inpiduals and groups, and is more suitable for solving multi-criteria decision-making problems with conflicts of interest.
　　二、VIKOR模型的构建
　　VIKOR model construction
　　一个决策评价模型主要由决策方案、评价属性和决策数据组成。所有的决策都至少包含两个及以上的方案供决策者选择，仅有一个方案就不叫决策了。其次，在选择方案时一定会有相应的评价指标。最后决策数据也是不可缺少的一项，它由评分者给出，并可通过多种形式表达。
　　除此之外，还有模糊数和模糊集之类更复杂的数据类型，它们更能表现出决策者的心理行为以及主观偏好。
　　除了上述三个板块，决策模型中一般还包含评价属性的权重。权重表示决策者的偏好程度，比如决策者想在几家供应商中选择一家来采购一批零部件，其零部件的质量和价格都是考虑因素，但相比价格，决策者更看重质量。因此，质量的评价指标权重比价格的指标权重更大。
　　A decision evaluation model is mainly composed of decision plans, evaluation attributes and decision data. All decisions include at least two or more options for decision-makers to choose, and only one option is not called a decision. Secondly, there must be corresponding evaluation indicators when choosing a plan. The final decision data is also an indispensable item, which is given by the scorer and can be expressed in many forms.
　　In addition, there are more complex data types such as fuzzy numbers and fuzzy sets, which can better show the psychological behavior and subjective preferences of decision makers.
　　In addition to the above three sections, the decision model generally also contains the weight of the evaluation attribute. The weight indicates the degree of preference of the decision maker. For example, the decision maker wants to choose one of several suppliers to purchase a batch of parts. The quality and price of the parts are considered factors, but the decision makers value quality more than price. Therefore, the evaluation index weight of quality is greater than the index weight of price.
　　下面进行模型举例：
　　设置M={1，2，….m}，N={1，2，….n}
　　A={A1,A2,…Am}表示m个备选方案的集合，其中Ai表示第i个备选方案，i∈m；
　　C={C1,C2,…Cn}表示n个属性的集合，其中Cj表示第j个属性，j∈n;
　　ω={ω1，ω2，…ωn}表示属性的权重向量，其中ωj为属性Cj的权重，满足ωj≥0，
　　且
　　The following model examples:
　　Set M={1,2,….m}, N={1,2,….n}
　　A={A1,A2,...Am} represents a set of m alternatives, where Ai represents the i-th alternative, i∈m;
　　C={C1,C2,...Cn} represents a set of n attributes, where Cj represents the jth attribute, j∈n;
　　ω={ω1,ω2,...ωn} represents the weight vector of the attribute, where ωj is the weight of the attribute Cj, which satisfies ωj≥0,
　　and
　　Xij为方案Ai对于属性Cj的结果。
　　以下即为构建的决策评价矩阵表：
　　Xij is the result of scheme Ai for attribute Cj.
　　The following is the constructed decision evaluation matrix table:
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