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Share interest, spread happiness, increase knowledge, and leave beautiful.

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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博士论文《基于模糊评价信息的多属性决策方法研究》预备知识部分内容，接下来我们开始今天的学习吧！

Today's small edition will bring you the preliminary knowledge of the doctoral dissertation Research on Multi attribute Decision Making Methods Based on Fuzzy Evaluation Information from three parts: mind mapping, intensive reading and knowledge supplement. Let's start today's study!

“

思维导图

下图是本节内容的思维导图：

The following figure is the mind map of this section:

“

精读内容

在第三节 “基于毕达哥拉斯不确定语言信息的多属性决策方法” 内容中，作者首先阐述了模糊不确定语言集的发展过程及其研究现状； 最开始有不同学者将模糊集和不确定语言相结合，提出模糊语言集，然后就是直觉模糊集、毕达哥拉斯模糊集和不确定语言之间的结合，但是，都存在着一些缺陷或者相关研究不足的问题，因此本文提出新的毕达哥拉斯集成算子，并将其应用到多属性决策问题中。本节内容是回顾一些基础知识，包括毕达哥拉斯不确定语言集和一些基础融合算子。

In the third section, "multi-attribute decision-making methods based on Pythagorean uncertain linguistic information", the author first describes the development process and research status of fuzzy uncertain linguistic sets; At the beginning, different students combined fuzzy sets and uncertain languages, and proposed fuzzy language sets, and then the combination of intuitionistic fuzzy sets, Pythagorean fuzzy sets and uncertain languages. However, there are some defects or related research deficiencies. Therefore, this paper proposes a new Pythagorean integration operator and applies it to multi-attribute decision-making problems. This section reviews some basic knowledge, including Pythagorean uncertain language set and some basic fusion operators.

毕达哥拉斯不确定语言集

作者首先介绍了毕达哥拉斯不确定语言变量的运算法则，并给出两个毕达哥拉斯不确定语言变量之间的距离测度公式，如下所示：

The author first introduces the operation rules of Pythagorean uncertain language variables, and gives the distance measure formula between two Pythagorean uncertain language variables, as shown below:

接着，作者给出了毕达哥拉斯不确定变量的比较法则定义如下所示：

Then, the author defines the comparison rule of Pythagorean uncertain variables as follows:

幂算子和 MM 算子

作者之前已经对PA加权平均集成算子的定义进行了详细介绍，如下所示， 在此部分就不再继续阐述。

The author has previously introduced the definition of PA weighted average integration operator in detail, as shown below, and will not continue to elaborate in this section.

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知识补充

上文中提到的语言变量的具体定义及相关知识，我们不太熟悉，接下来就让我们一起来了解一下吧！

We are not familiar with the specific definitions and related knowledge of language variables mentioned above. Let's take a look!

语言变量：

人类的语言可分为两种:自然语言和形式语言。自然语言的语意丰富、灵活，有时具有模糊性。例如“一朵美丽的花”这句话就具有模糊性，这朵花究竟有多美丽，也许各人有各人的看法。这种带有模糊性的自然语言称为模糊语言，例如长、短、大、小、年轻、年老等词语。而形式语言则有严格的语法规则和语意，不存在任何的模糊性和二意性。譬如通常的计算机语言就是形式语言。

Language variable:

Human language can be divided into two kinds: natural language and formal language. The meaning of natural language is rich, flexible and sometimes vague. For example, the sentence "a beautiful flower" is ambiguous. Maybe everyone has their own opinion on how beautiful the flower is. This kind of natural language with fuzziness is called fuzzy language, such as long, short, big, small, young, old and other words. However, formal language has strict grammatical rules and semantics, without any ambiguity or ambiguity. For example, the common computer language is formal language.

蕴含关系：

1.语言变量是自然语言中的词或句，它的取值不是通常的数，而是用模糊语言表示的模糊集合。例如“年龄”就可以是一个模糊语言变量，其取值为“年幼”、“年轻”、“年老”等模糊集合。

2.如何定义一个语言变量（四要素）

定义变量名称。

定义变量的论域。

定义变量的语言值（每个语言值是定义在变量论域上的一个模糊集合)

定义每个模糊集合的隶属函数。

Implication relation:

1. Language variable is a word or sentence in natural language. Its value is not a normal number, but a fuzzy set expressed by fuzzy language. For example, "age" can be a fuzzy language variable, and its values are "young", "young", "old" and other fuzzy sets.

2. How to define a language variable (four elements)

Define the variable name.

Define the universe of variables.

Define the linguistic values of variables (each linguistic value is a fuzzy set defined in the variable universe)

Defined the membership function of each fuzzy set.

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参考资料：DeeL翻译，百度百科

参考文献：[1]赵红梅. 基于模糊评价信息的多属性决策方法研究 [D]. 北京交通大学, 2021.

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