小源笔记（三十）：Matlab入门学习之VIKOR方法概述--粉丝服务平台-粉丝头条-fensifuwu.com

小源笔记（三十）：Matlab入门学习之VIKOR方法概述

科技 09-16 来源： LearningYard学苑

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一、VIKOR方法简介

VIKOR方法是一种基于理想点解的多属性决策方法，其基本思想是基于最佳化妥协解方法确定理想解和负理想解，然后根据各个备选方案的评价值与理想方案的接近程度选择最优方案。VIKOR方法求得的解依据两属性间互相让步的结果求得折中解。得到带有优先级的折中方案更接近于理想方案，它的特点就是能够得到最接近理想方案的妥协解，做到了最大化群体效益与最小化个体损失这一方法得到的方案更容易被决策者接受。

VIKOR method is a multi-attribute decision-making method based on ideal point solution. best plan. The solution obtained by the VIKOR method obtains a compromise solution based on the results of mutual concessions between the two attributes. The compromise solution with priority is closer to the ideal solution. Its characteristic is that it can obtain the compromise solution that is closest to the ideal solution, and the solution obtained by maximizing the group benefit and minimizing the individual loss is easier to be decided. are accepted.

基本步骤：

首先要将决策矩阵规范化处理，得到效益性指标和成本性指标，其次要计算到理想解和负理想解的距离，比值最后算出利益比率。根据计算出的利益比率进行排序，值最小的方案为优化方案。

The basic steps:

First, the decision matrix should be normalized to obtain the benefit index and cost index. Second, the distance to the ideal solution and the negative ideal solution should be calculated, and the ratio should be calculated to calculate the benefit ratio. Sort according to the calculated benefit ratio, and the solution with the smallest value is the optimal solution.

二、VIKOR方法和TOPSIS方法对比分析

（1）聚合函数。

TOPSIS和VIKOR的区别之一在于聚合函数。TOPSIS是基于距离理想解的距离的集合，VIKOR方法在TOPSIS方法的基础上提出了一个具有优势率的折衷方案。在TOPSIS方法中，不仅要考虑到与正理想解的最近距离，而且考虑到与负理想解的最长距离，从而确定最优解，以最大限度地提高效益。但TOPSIS 中的这些距离只是简单地求和，没有考虑它们的相对重要性，而在VIKOR中决策者会根据自身需求确定其重要性。

(1) Aggregate function.

One of the differences between TOPSIS and VIKOR is the aggregation function. TOPSIS is based on the set of distances from the ideal solution, and the VIKOR method proposes a compromise with an odds ratio based on the TOPSIS method. In the TOPSIS method, not only the closest distance to the positive ideal solution, but also the longest distance to the negative ideal solution is considered to determine the optimal solution to maximize the benefit. But these distances in TOPSIS are simply summed without considering their relative importance, whereas in VIKOR decision makers determine their importance according to their own needs.

（2）决策主观性。

VIKOR方法相比TOPSIS方法多了一个决策机制系数，它可以使决策者做出更激进或更保守的决策。TOPSIS方法的过程没有纳入任何主观因素，更适合要求结果完全客观的决策环境。

(2) The subjectivity of decision-making.

Compared with the TOPSIS method, the VIKOR method has one more decision-making mechanism coefficient, which can enable decision-makers to make more aggressive or conservative decisions. The process of the TOPSIS method does not incorporate any subjective factors and is more suitable for decision-making environments that require completely objective results.

（3）方案排序。

VIKOR方法的独特优势在于可以得到带有优先级的折衷方案，这使得通过VIKOR排序后的最佳方案可能不止一个。而TOPSIS方法只能得到唯一最优解，毕竟它的过程是完全客观的。

(3) Program sorting.

The unique advantage of the VIKOR method is that it can obtain a compromise solution with priority, which makes it possible that there may be more than one optimal solution sorted by VIKOR. The TOPSIS method can only get the only optimal solution, after all, its process is completely objective.

三、构建VIKOR评价模型

VIKOR方法流程图如上所示，通常来说，我们讨论的是红框内的内容，核心是带权重的距离公式，一组得到期望值，一组得到遗憾值。

The flowchart of the VIKOR method is shown above. Generally speaking, we are talking about the content in the red box. The core is the weighted distance formula. One group gets the expected value, and the other group gets the regret value.

接下来以实数为例，构建由以下要素组成的决策评价模型：

Next, take real numbers as an example to build a decision evaluation model consisting of the following elements: