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亲爱的您，
这里是LearningYard学苑！
今天小编给大家带来期刊论文精读，
欢迎您的用心访问！
本期推文阅读时长大约6分钟，请您耐心阅读。
Share interest, spread happiness, increase knowledge, and leave beautiful.
Dear you,
this is the LearningYard Academy!
Today, the editor brings you intensive reading of journal papers,
welcome your visit!
This tweet usually takes about 6 minutes to read. Please be patient and read.
今天小编将从思维导图、精读内容、知识补充三个板块为大家带来论文《属性关联的双极容度多属性决策 VIKOR方法》计算与分析，接下来我们开始今天的学习吧！
Today, the editor will bring you the calculation and analysis of the paper "VIKOR Method of Bipolar Tolerance Multi-attribute Decision Making of Attribute Association" from the three parts of mind map, intensive reading content and knowledge supplement. Next, let's start today's study!
思维导图
本节内容思维导图如下所示：
A mind map of the contents of this section is shown below.
精读内容
在计算过程中，作者考虑属性关联的关系，采用双极容度对交互的属性的权重进行建模测量，而在求解属性的权重之前，需要确定常权情况下双极容度的Shapley值，作者采用AHP方法确定各个属性的shapley值。
In the calculation process, the author considers the relationship between attributes, and adopts bipolar capacity to model and measure the weight of interactive attributes. Before solving the weight of attributes, it is necessary to determine the Shapley value of bipolar capacity under constant weight. The author uses AHP method to determine the Shapley value of each attribute.
代码如下：
The code is as follows:
结果如图所示：
The results are shown in the figure:
知识补充
我们在学习本节内容的过程中需要将得到的各属性的Shapley值代入Lingo软件中计算，接下来让我们一起来了解一下吧!
In the process of learning this section, we need to substitute the Shapley values of each attribute into Lingo software for calculation. Next, let's have a look!
LINGO是Linear Interactive and General Optimizer的缩写，即“交互式的线性和通用优化求解器”，由美国LINDO系统公司（Lindo System Inc.）推出的，可以用于求解非线性规划，也可以用于一些线性和非线性方程组的求解等，功能十分强大，是求解优化模型的最佳选择。
LINGO is the abbreviation of Linear Interactive and General Optimizer, that is, "Interactive Linear and General Optimization Solver", which was launched by LINDO System Inc. of the United States. It can be used to solve nonlinear programming, and can also be used to solve some linear and nonlinear equations. It has very powerful functions and is the best choice for solving optimization models.
其特色在于内置建模语言，提供十几个内部函数，可以允许决策变量是整数（即整数规划，包括 0-1 整数规划），方便灵活，而且执行速度非常快。能方便与EXCEL，数据库等其他软件交换数据。LINGO18.0为最新版本。
Its feature is that it has a built-in modeling language, provides more than ten internal functions, and allows the decision variables to be integers (that is, integer programming, including 0-1 integer programming), which is convenient and flexible, and the execution speed is very fast. It is convenient to exchange data with EXCEL, database and other software. LINGO18.0 is the latest version.
一般地，使用LINGO 求解运筹学问题可以分为以下两个步骤来完成：1）根据实际问题，建立数学模型，即使用数学建模的方法建立优化模型；2）根据优化模型，利用LINGO 来求解模型。主要是根据LINGO软件，把数学模型转译成计算机语言，借助于计算机来求解。
Generally, using LINGO to solve operational research problems can be divided into the following two steps: 1) According to actual problems, establish mathematical models, that is, use mathematical modeling methods to establish optimization models; 2) According to the optimization model, LINGO is used to solve the model. Mainly according to LINGO software, the mathematical model is translated into computer language and solved by computer.
今天的分享就到这里了。
如果您对今天的文章有独特的想法，
欢迎给我们留言，
让我们相约明天，
祝您今天过得开心快乐！
That's it for today's sharing.
If you have a unique idea about today’s article,
welcome to leave us a message,
let us meet tomorrow,
I wish you a nice day today!
参考资料：DeepL翻译、百度百科
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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