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！
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》步骤四，接下来我们开始今天的学习吧！
Today, the editor will bring you the paper "The Bipolar Tolerance Multiple Attribute Decision Making VIKOR Method of Attribute Association" from three sections: mind mapping, intensive reading content, and knowledge supplement. Step 4, let's begin 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
在上期推文中，搞清楚了最大熵模型中关于最大熵定义中为何要用期望来表示约束条件，接着咱们一起来看看条件熵的概念。
In the previous tweet, we clarified why expectations are used to represent constraints in the definition of maximum entropy in the maximum entropy model. Next, let's take a look at the concept of conditional entropy.
一、为什么要使用条件熵
1、 Why use conditional entropy
条件熵就是在已知X的情况下，Y的概率分布所对应的熵。这里的条件其实就是X，不同条件所对应的类别就是输出变量Y。那么为什么要用条件熵，而不能写成联合熵呢？
Conditional entropy is the entropy corresponding to the probability distribution of Y when X is known. The condition here is actually X, and the category corresponding to different conditions is the output variable Y. So why use conditional entropy instead of joint entropy?
最大熵模型实际上是判别方法，判别方法就是要得出条件概率分布，就是要得出满足maxH(P)的P(Y|X)。
The maximum entropy model is actually a discrimination method. The discrimination method is to get the conditional probability distribution, which is to get P (Y | X) that meets maxH (P).
二、条件熵公式的变换
对于一个输入变量Xi，那么它对应的条件熵是什么呢？对于这个熵而言，我们可以乘以每个输入变量对应的概率P(xi) ，然后加权求和。
2、 Transformation of Conditional Entropy Formula
What is the conditional entropy corresponding to an input variable Xi? For this entropy, we can multiply it by the probability P (xi) corresponding to each input variable, and then weighted sum it up.
这样我们就把条件熵的公式推导出来咯，看到这里，可以比对一下，是不是一模一样。
So we can deduce the formula of conditional entropy. See here, we can compare whether it is the same.
知识补充
上文中，我们学习了公式的相关含义，接下来，和小编一起了解一下撰写论文时对公式输入的技巧吧！
In the previous text, we learned the relevant meanings of formulas. Next, let's learn about the skills of inputting formulas when writing a paper with the editor!
写论文中排版不是容易的事，尤其是需要处理较多公式的时候，特别是在公式修改，“牵一发而动全身”，最好是可以在修改后自动更新，可以节省大量的手动修改的时间。今天给大家介绍一下公式自动编号和更新。
Typography in writing a paper is not an easy task, especially when dealing with a large number of formulas, especially when modifying formulas. It is best to update them automatically after modification, which can save a lot of manual editing time. Today, we will introduce formula automatic numbering and updating.
毕业论文的公式编号是需要带有章节号码的，这个如果手动更改是很麻烦的。首先，在 Word 中插入章节符，在章节正文的上方插入一个 MathType 分节符：Word 功能栏-MathType 菜单-插入分节符。
The formula number of the graduation thesis needs to be accompanied by a chapter number, which can be troublesome to manually change. Firstly, insert a chapter break in Word and a MathType section break above the main body of the chapter: Word Function Bar - MathType Menu - Insert Section Break.
其次，在对话框选择新段落，输入章节号，下面我输入的是第 3 章第 4 节。
Secondly, in the dialog box, select a new paragraph and enter the chapter number. Below, I will enter Chapter 3, Section 4.
然后，选择 MathType 菜单，设置好公式编号的格式：MathType-公式编号格式-简单，选择相应即可。
Then, select the MathType menu and set the format for the formula number: MathType - Formula Number Format - Simple, select the corresponding option.
最后，MathType-插入公式编号，编号就会出现在公式的后面。
Finally, MathType - inserts the formula number, which will appear after the formula.
论文没有一次性完成的，往往需要一次又一次的修改，与之相应的公式编号也应该随着章节的变化而更新。公式较多时，手动修改是不可能的，一方面消耗太多精力，另一方面出错的概率也比较高。
Papers are not completed in one go and often require repeated revisions, and the corresponding formula numbers should also be updated with changes in chapters. When there are many formulas, manual modification is impossible. On the one hand, it consumes too much energy, and on the other hand, the probability of errors is also relatively high.
点击 MathType 菜单-更新公式编号。
Click on the MathType menu - Update Formula Number.
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：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.
文案 |Yuan
排版 |Yuan
审核 |Wang