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》案例分析，接下来我们开始今天的学习吧！
Today's small edition will bring you the case study of the paper "Bipolar Tolerance Multi Attribute Decision Making VIKOR Method of Attribute Association" from three parts: mind mapping, intensive reading and knowledge supplement. 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
本期推文小编将和大家一起继续对案例进行详细解读分析，在考虑属性间的关联关系计算权重后，我们考虑根据双极容度的choquet积分算子的公式，求解方案的贴近度Si和Ri。
The editor of this tweet will continue to analyze the case in detail with you. After considering the correlation between attributes to calculate the weight, we consider solving the closeness degree Si and Ri of the scheme according to the formula of the choquet integral operator of the bipolar tolerance.
但是，小编在理解以上公式的过程中，我发现该部分内容涉及到choquet积分和模糊测度的相关知识，上期推文中我们学习和探索了关于模糊积分的知识点，本期我们将学习模糊测度相关公式及内容。
However, in the process of understanding the above formulas, I found that this part of the content involves the knowledge of choquet integral and fuzzy measure. In the last tweet, we learned and explored the knowledge points about fuzzy integral. In this issue, we will learn the relevant formulas and contents of fuzzy measure.
上图中对于定理的理解，我们可以举例来分析，以便我们更好地理解和消化知识点！
For the understanding of the theorem in the above figure, we can analyze it with examples, so that we can better understand and digest the knowledge points!
知识补充
我们对本节内容中的模糊测度、gλ模糊测度进行了详细的学习和分析，在这过程中我们提到了正则测度，接下来让我们一起来了解一下吧！
We discuss the fuzzy measure, g λ Fuzzy measures have been studied and analyzed in detail. In the process, we mentioned regular measures. Let's take a look!
正则测度(regular measure)一种比较规则的测度。既外正则又内正则的测度称为正则测度。
Regular measure is a measure that compares rules. Measures that are both outer regular and inner regular are called regular measures.
测度，是数学术语，释义是构造一个集函数，它能赋予实数集簇М中的每一个集合E一个非负扩充实数m(E)。我们将此集函数称为E的测度。 测度有计数测度、勒贝格测度、哈尔测度、概率测度等。
Measure is a mathematical term. Its definition is to construct a set function, which can give a real number set cluster М Each set E in is a nonnegative extended real number m (E). We call this set function the measure of E. Measures include counting measure, Lebesgue measure, Hal measure, probability measure, etc.
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、哔哩哔哩
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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