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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。
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Dear you,
this is the LearningYard Academy!
Today, the editor brings you an interpretation of the doctoral thesis,
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期刊论文《犹豫模糊语言距离测度及其在多属性决策中的应用》第一节和第二节的内容，接下来我们开始今天的学习吧！
Today, the editor will introduce the first and second sections of the journal paper "Hesitation Fuzzy Language Distance Measurement and Its Application in Multi attribute Decision Making" from three sections: mind mapping, intensive reading content, and knowledge supplementation. Let's start today's learning!
01
思维导图
本节内容的思维导图如下所示：
The mind map of this section is as follows:
02
精读内容
一、犹豫模糊语言集相关定义
在介绍现有犹豫模糊语言集距离测度的局限性之前，作者首先列举了关于犹豫模糊语言集的相关定义，包含四个方面的内容：由于模糊语言集的数学表达式、犹 豫 模 糊 语 言 集 的 偏 序、犹豫模糊语言集距离测度的性质以及犹豫模糊语言数的广义豪斯多夫距离公式。如下所示：
1、 Definition of Hesitative Fuzzy Language Set
Before introducing the limitations of distance measures in existing hesitant fuzzy language sets, the author first lists the relevant definitions of hesitant fuzzy language sets, including four aspects: the mathematical expression of hesitant fuzzy language sets, the partial order of hesitant fuzzy language sets, the properties of distance measures in hesitant fuzzy language sets, and the generalized Hausdorff distance formula for hesitant fuzzy language numbers. As follows:
二、现有犹豫模糊语言距离测度的局限性
接下来，通过理解和分析上述犹豫模糊语言距离测度，虽然现有犹豫模糊语言距离测度的具有一定的合理性和度量优势，但仍然存在如下几个方面的局限性:
2、 The limitations of existing distance measures for hesitant fuzzy language
Next, by understanding and analyzing the above hesitant fuzzy language distance measures, although existing hesitant fuzzy language distance measures have certain rationality and measurement advantages, there are still limitations in the following aspects:
三、新型犹豫模糊语言距离测度
最后，作者基于上文描述的现有有犹豫模糊语言距离测度的不足，进一步提出了犹豫模糊语言集的犹豫度定义；并且，还给出了一系列更为合理的新型犹豫模糊语言距离测度方法。如下所示：
3、A New Distance Measure for Hesitative Fuzzy Language
Finally, based on the shortcomings of the existing distance measure for hesitant fuzzy languages described above, the author further proposes a definition of hesitant degree for hesitant fuzzy language sets; Moreover, a series of more reasonable new hesitant fuzzy language distance measurement methods have been proposed. As follows:
03
知识补充
在上文内容中涉及到了Hamming距离，接下来和小编一起来了解一下吧！
In the previous content, the Hamming distance was mentioned. Let's take a look together with the editor!
Hamming距离是两个向量之间不同的值的数量。它通常用于比较两个等长的二进制字符串。它也可用于字符串，通过计算彼此不同的字符数来比较它们之间的相似程度。它的缺点是：当两个向量的长度不相等时，Hamming距离很难使用。你会想把相同长度的向量相互比较，以了解哪些位置不匹配。
Hamming distance is the number of different values between two vectors. It is usually used to compare two binary strings of equal length. It can also be used for strings to compare their similarity by calculating the number of characters that are different from each other. Its disadvantage is that when the lengths of two vectors are not equal, the Hamming distance is difficult to use. You may want to compare vectors of the same length with each other to understand which positions do not match.
此外，只要它们不同或相等，它就不考虑实际值。因此，当幅度是一个重要的衡量标准时，不建议使用这种距离衡量标准。
Furthermore, as long as they are different or equal, it does not consider the actual value. Therefore, when amplitude is an important measure, it is not recommended to use this distance measure.
使用案例：典型的用例包括当数据通过计算机网络传输时的错误纠正/检测。它可以用来确定二进制字中失真的比特数，作为估计错误的一种方法。此外，你也可以用Hamming距离来测量分类变量之间的距离。
Use case: Typical use cases include error correction/detection when data is transmitted through a computer network. It can be used to determine the number of distorted bits in binary words as a method of estimating errors. In addition, you can also use Hamming distance to measure the distance between categorical variable.
今天的分享就到这里了。
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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] 吴双胜, 林杰, 杨玉舒等. 犹豫模糊语言距离测度及其1在多属性决策中的应用 [J]. 运筹与管理, 2023, 32(2): 61-67.
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