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今天小编为您带来精读复刻论文《基于CWPHM算子和C-DEMATEL的语言型多属性决策方法》预备知识。
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Share interest, spread happiness,
increase knowledge, and leave beautiful.
Dear, this is the LearingYard Academy!
Today, the editor brings the "intensive reading replica paper 'A linguistic Multi-Attribute Decision-Making approach based on the CWPHM operator and C-DEMATEL' for prerequisites".
Welcome to visit!
一、内容摘要（Summary of Content）
本期推文将从思维导图、精读内容、知识补充三个方面介绍精读复刻论文《基于CWPHM算子和C-DEMATEL的语言型多属性决策方法》的预备知识。
This tweets will introduce the prerequisites of the intensively read replica paper "A linguistic Multi-Attribute Decision-Making approach based on the CWPHM operator and C-DEMATEL" in terms of mind mapping, intensive reading content, and knowledge supplementation.
二、思维导图（Mind Maps）
三、精读内容（Intensive reading content）
在本论文的预备知识部分，作者首先简单介绍了一下云模型：该模型在将定性信息转换为不确定数据时，不仅能够依据期望、熵和超熵等三个数字特征来考虑定性信息的模糊性和随机性，还能够依据正太分布运算法则来避免决策信息的丢失。然后作者介绍了相关的云模型的一些定义。
In the prerequisites of this paper, the author first briefly introduces the cloud model: when converting qualitative information into uncertain data, the model can not only consider the ambiguity and randomness of qualitative information according to the three numerical characteristics of expectation, entropy and superentropy, but also avoid the loss of decision-making information according to the positive and Pacific distribution algorithm. The author then presents some definitions of the relevant cloud model.
根据定义1，元素x的隶属度y在给定论域U上的分布为云，且每一组(x, y)可以看成一个云滴；定义2则定义语言短语h，的精确数得分及其计算式；定义3则定义语言短语转换后的云计算过程；定义4则定义任意两朵云之间的运算法则。
According to definition 1, the membership of element x y is distributed as a cloud over a given domain U, and each group (x, y) can be seen as a cloud droplet; Definition 2 defines the exact number score of the language phrase h, and its calculation formula; Definition 3 defines the cloud computing process after language phrase conversion; Definition 4 defines the algorithm between any two clouds.
为了对云的大小进行比较，定义5则给出云总计分的定义。为了对云之间的距离进行测度，定义6则给出云距离的定义。为了对云之间的距离进行规范化处理，本文在定义6的基础上，定义7则给出云的规范化距离的定义。
For the purpose of comparing the size of the clouds, definition 5 gives the definition of the total score of the clouds. To measure the distance between clouds, definition 6 gives the definition of cloud distance. In order to normalize the distance between clouds, this paper gives the definition of the normalized distance of clouds on the basis of definition 6, and definition 7.
四、知识补充——汉明距离（Knowledge Supplement – Hamming Distance）
汉明距离是使用在数据传输差错控制编码里面的，汉明距离是一个概念，它表示两个（相同长度）字符串对应位置的不同字符的数量，我们以d（x,y）表示两个字x，y之间的汉明距离。对两个字符串进行异或运算，并统计结果为1的个数，那么这个数就是汉明距离。
Hamming distance is used in data transmission error control encoding, Hamming distance is a concept that represents the number of different characters in the corresponding position of two (same length) strings, we use d(x,y) to denote the Hamming distance between two words x,y. XOR operations are performed on two strings, and the number of the resulting result is 1, then this number is the Hamming distance.
汉明距离是以理查德·卫斯里·汉明的名字命名的。在信息论中，两个等长字符串之间的汉明距离是两个字符串对应位置的不同字符的个数。换句话说，它就是将一个字符串变换成另外一个字符串所需要替换的字符个数。例如：1011101与1001001之间的汉明距离是2。
The Hamming distance is named after Richard Wesley Hamming. In information theory, the Hamming distance between two equal-length strings is the number of different characters at the corresponding positions of the two strings. In other words, it's the number of characters that need to be replaced to convert one string to another. For example, the Hamming distance between 1011101 and 1001001 is 2.
汉明距离更多的用于信号处理，表明一个信号变成另一个信号需要的最小操作（替换位），实际中就是比较两个比特串有多少个位不一样，简洁的操作时就是两个比特串进行异或之后包含1的个数。汉明距离在图像处理领域也有着广泛的应用，是比较二进制图像非常有效的手段。其在包括信息论、编码理论、密码学等领域都有应用。但是，如果要比较两个不同长度的字符串，不仅要进行替换，而且要进行插入与删除的运算，在这种场合下，通常使用更加复杂的编辑距离等算法。
Hamming distance is more used for signal processing, indicating that the minimum operation (substitution bit) required for one signal to become another signal is actually to compare how many bits are different between two bit strings, and in the case of a simple operation, the number of bits that the two bit strings are XC or then contain 1. Hamming distance also has this wide application in the field of image processing, and is a very effective means of comparing binary images. It has applications in information theory, coding theory, cryptography and other fields. However, if you want to compare two strings of different lengths, you need to not only replace, but also insert and delete, in which case more complex algorithms such as edit distance are often used.
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参考资料：谷歌翻译、百度百科
参考文献：
王伟明, 徐海燕, 朱建军等. 基于CWPHM算子和C-DEMATEL的语言型多属性决策方法 [J/OL]. 中国管理科学, 2023, 1(1): 1-13.
本文由LearningYard学苑整理并发出，如有侵权请在后台留言！
文案| Ann
排版| Ann
审核| 王楠鑫